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GRADE 11 PRACTICE

Physics Problems: Oscillations and waves, Grade 11

Mechanical, electromagnetic vibrations and wave connections.

48 problems across 4 sub-topics
Practise in the interactive mode

Here the conditions and analysis of the solution can be read without an account. In the simulator, you need to collect the same analyzes yourself: “Given,” formulas, order of steps and answer.

Problem statements

The answer options are there to check against, and the walkthrough opens under each problem.

48 problems
Position in this set: 1 from 48

Problem #12

Mechanical oscillations

Determine the period and frequency of a string pendulum of length 1\,\text{м}. How many oscillations will he make in 30\,\text{с}?

Answer options

  1. \left(20\,\text{с};\ 5\,\text{Гц};\ 150\,\text{колебаний}\right)
  2. \left(2\,\text{с};\ 0{,}5\,\text{Гц};\ 15\,\text{колебаний}\right)
  3. \left(1\,\text{с};\ 0{,}25\,\text{Гц};\ 7{,}5\,\text{колебаний}\right)
  4. \left(4\,\text{с};\ 1\,\text{Гц};\ 30\,\text{колебаний}\right)
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Given
\ell
1\,\text{м}
t
30\,\text{с}
g
10\,\tfrac{\text{м}}{\text{с}^{2}}
Find

T\nun

  1. T = 2\pi\sqrt{\dfrac{\ell}{g}}T = 2\cdot 3{,}14\sqrt{\dfrac{1}{10}}T = 2\,\text{с}
  2. \nu = \dfrac{1}{T}\nu = \dfrac{1}{2}\nu = 0{,}5\,\text{Гц}
  3. n = \dfrac{t}{T}n = \dfrac{30}{2}n = 15

AnswerT = 2\,\text{с}\nu = 0{,}5\,\text{Гц}n = 15

Position in this set: 2 from 48

Problem #13

Mechanical oscillations

Weight of the spring pendulum 40\,\text{г}, spring stiffness 20\,\text{Н/м}. Define period, frequency and time 25 hesitation.

Answer options

  1. \left(0{,}56\,\text{с};\ 7{,}12\,\text{Гц};\ 14\,\text{с}\right)
  2. \left(2{,}8\,\text{с};\ 35{,}6\,\text{Гц};\ 70\,\text{с}\right)
  3. \left(0{,}28\,\text{с};\ 3{,}56\,\text{Гц};\ 7\,\text{с}\right)
  4. \left(0{,}14\,\text{с};\ 1{,}78\,\text{Гц};\ 3{,}5\,\text{с}\right)
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Given
m
40\,\text{г}0{,}04\,\text{кг}
k
20\,\tfrac{\text{Н}}{\text{м}}
n
25
Find

T\nut

  1. T = 2\pi\sqrt{\dfrac{m}{k}}T = 2\cdot 3{,}14\sqrt{\dfrac{0{,}04}{20}}T = 0{,}28\,\text{с}
  2. \nu = \dfrac{1}{T}\nu = \dfrac{1}{0{,}28}\nu = 3{,}56\,\text{Гц}
  3. t = nTt = 25\cdot 0{,}28t = 7\,\text{с}

AnswerT = 0{,}28\,\text{с}\nu = 3{,}56\,\text{Гц}t = 7\,\text{с}

Position in this set: 3 from 48

Problem #14

Mechanical oscillations

When a load of mass is suspended from a spring 800\,\text{г}, she stretched out on 2\,\text{см}. Determine the frequency of vibration of the load.

Answer options

  1. 1{,}78\,\text{Гц}
  2. 7{,}12\,\text{Гц}
  3. 35{,}6\,\text{Гц}
  4. 3{,}56\,\text{Гц}
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Given
m
800\,\text{г}0{,}8\,\text{кг}
\Delta\ell
2\,\text{см}0{,}02\,\text{м}
g
10\,\tfrac{\text{м}}{\text{с}^{2}}
Find

\nu

  1. mg = k\,\Delta\ell\ \Rightarrow\ k = \dfrac{mg}{\Delta\ell}
  2. T = 2\pi\sqrt{\dfrac{m}{k}} = 2\pi\sqrt{\dfrac{\Delta\ell}{g}}T = 2\cdot 3{,}14\sqrt{\dfrac{0{,}02}{10}}T = 0{,}28\,\text{с}

    The mass contracts - the period depends only on the stretch of the spring.

  3. \nu = \dfrac{1}{T}\nu = \dfrac{1}{0{,}28}\nu = 3{,}56\,\text{Гц}

Answer\nu = 3{,}56\,\text{Гц}

Position in this set: 4 from 48

Problem #15

Mechanical oscillations

For 5\,\text{с} spring pendulum made 8 hesitation. Determine the mass of the load if the spring stiffness 25\,\text{Н/м}. Is there enough data to find a path in the first 0{,}1\,\text{с} at amplitude 10\,\text{см}?

Answer options

  1. \left(0{,}25\,\text{кг};\ \text{для пути нужна начальная фаза}\right)
  2. \left(0{,}40\,\text{кг};\ 0{,}10\,\text{м}\right)
  3. \left(0{,}25\,\text{кг};\ 0{,}20\,\text{м}\right)
  4. \left(1\,\text{кг};\ \text{для пути данных достаточно}\right)
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Given
t
5\,\text{с}
n
8
k
25\,\tfrac{\text{Н}}{\text{м}}
A
10\,\text{см}0{,}1\,\text{м}
Find

m\text{enough whether data for ways}

  1. T = \dfrac{t}{n}T = \dfrac{5}{8}T = 0{,}625\,\text{с}
  2. T = 2\pi\sqrt{\dfrac{m}{k}}\ \Rightarrow\ T^{2} = \dfrac{4\pi^{2}m}{k}\ \Rightarrow\ m = \dfrac{T^{2}k}{4\pi^{2}}m = \dfrac{0{,}625^{2}\cdot 25}{4\cdot 3{,}14^{2}}m = 0{,}25\,\text{кг}
  3. x=A\cos(\omega t+\varphi_0)

    The path for a part of the period depends on the initial phase. Amplitude and period do not determine the position and direction of movement at the initial moment.

Answerm = 0{,}25\,\text{кг}\text{For ways needed Initial phase}

Position in this set: 5 from 48

Problem #16

Mechanical oscillations

Load weight 2\,\text{кг} fluctuates on a spring stiffness 50\,\text{Н/м} with amplitude 5\,\text{см}. Determine possible coordinates through 0{,}15\,\text{с} in two cases: a) the load is released from position x = +A without initial speed; b) the load passes x = 0 in the positive direction. Also find the velocity modulus at the point x=2\,\text{см}.

Answer options

  1. \left(0{,}366\,\text{м};\ 0{,}341\,\text{м};\ 2{,}3\,\text{м/с}\right)
  2. \left(0{,}0366\,\text{м};\ 0{,}0341\,\text{м};\ 0{,}23\,\text{м/с}\right)
  3. \left(0{,}0183\,\text{м};\ 0{,}01705\,\text{м};\ 0{,}115\,\text{м/с}\right)
  4. \left(0{,}0732\,\text{м};\ 0{,}0682\,\text{м};\ 0{,}46\,\text{м/с}\right)
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Given
k
50\,\tfrac{\text{Н}}{\text{м}}
m
2\,\text{кг}
x_{\text{м}}
5\,\text{см}0{,}05\,\text{м}
t
0{,}15\,\text{с}
x
0{,}02\,\text{м}
Find

x_1x_2v

  1. \omega = \sqrt{\dfrac{k}{m}}\omega = \sqrt{\dfrac{50}{2}}\omega = 5\,\tfrac{1}{\text{с}}
  2. x_1 = x_{\text{м}}\cos\omega t0{,}05\cdot\cos\left(5\cdot 0{,}15\right) \approx 0{,}05\cdot 0{,}732x_1 = 0{,}0366\,\text{м}

    Counting from the extreme position.

  3. x_2 = x_{\text{м}}\sin\omega tx_2 = 0{,}05\cdot 0{,}682x_2 = 0{,}0341\,\text{м}

    Counting from the equilibrium position.

  4. \dfrac{kx_{\text{м}}^{2}}{2} = \dfrac{kx^{2}}{2} + \dfrac{mv^{2}}{2}\ \Rightarrow\ v = \sqrt{\dfrac{k\left(x_{\text{м}}^{2} - x^{2}\right)}{m}}v = \sqrt{\dfrac{50\left(0{,}05^{2} - 0{,}02^{2}\right)}{2}}v = 0{,}23\,\tfrac{\text{м}}{\text{с}}

Answerx_1 = 0{,}0366\,\text{м}x_2 = 0{,}0341\,\text{м}v = 0{,}23\,\tfrac{\text{м}}{\text{с}}

Position in this set: 6 from 48

Problem #17

Electromagnetic vibrations

Capacitor with capacity 125\,\text{пФ} charged to 400\,\text{В} and closed to a coil with inductance 20\,\text{мГн}. Determine the period, frequency and cyclic frequency, maximum charge and current. Neglect the loop resistance.

Answer options

  1. \left(1{,}987 \cdot 10^{-5}\,\text{с};\ 2{,}0132 \cdot 10^{5}\,\text{Гц};\ 1{,}2649 \cdot 10^{6}\,\text{рад/с};\ 1 \cdot 10^{-7}\,\text{Кл};\ 0{,}06324\,\text{А}\right)
  2. \left(9{,}935 \cdot 10^{-5}\,\text{с};\ 1{,}0066 \cdot 10^{6}\,\text{Гц};\ 6{,}3246 \cdot 10^{6}\,\text{рад/с};\ 5 \cdot 10^{-7}\,\text{Кл};\ 0{,}3162\,\text{А}\right)
  3. \left(9{,}935 \cdot 10^{-6}\,\text{с};\ 1{,}0066 \cdot 10^{5}\,\text{Гц};\ 6{,}3246 \cdot 10^{5}\,\text{рад/с};\ 5 \cdot 10^{-8}\,\text{Кл};\ 0{,}03162\,\text{А}\right)
  4. \left(4{,}9675 \cdot 10^{-6}\,\text{с};\ 50329\,\text{Гц};\ 3{,}1623 \cdot 10^{5}\,\text{рад/с};\ 2{,}5 \cdot 10^{-8}\,\text{Кл};\ 0{,}01581\,\text{А}\right)
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Given
C
125\,\text{пФ}125\cdot 10^{-12}\,\text{Ф}
U_{\text{м}}
400\,\text{В}
L
20\,\text{мГн}20\cdot 10^{-3}\,\text{Гн}
Find

T\nu\omegaq_{\text{м}}I_{\text{м}}

  1. T = 2\pi\sqrt{LC}T = 2\cdot 3{,}14\sqrt{20\cdot 10^{-3}\cdot 125\cdot 10^{-12}}T = 9{,}935\cdot10^{-6}\,\text{с}

    Thomson's formula.

  2. \nu = \dfrac{1}{T},\quad \omega = \dfrac{2\pi}{T}\nu = \dfrac{1}{9{,}935\cdot10^{-6}};\quad \omega = \dfrac{2\pi}{9{,}935\cdot10^{-6}}\nu = 1{,}0066\cdot10^5\,\text{Гц};\quad \nu = 6{,}3246\cdot10^5\,\text{рад/с}
  3. q_{\text{м}} = CU_{\text{м}}q_{\text{м}} = 125\cdot 10^{-12}\cdot 400q_{\text{м}} = 5\cdot 10^{-8}\,\text{Кл}
  4. I_{\text{м}} = q_{\text{м}}\omegaI_{\text{м}} = 5\cdot10^{-8}\cdot6{,}3246\cdot10^5I_{\text{м}} = 0{,}03162\,\text{А}

    Oscillation equations: q = q_m cos ωt, u = U_m cos ωt, i = I_m cos(ωt + π/2).

AnswerT=9{,}935\cdot10^{-6}\,\text{с}\nu=1{,}0066\cdot10^5\,\text{Гц}\omega=6{,}3246\cdot10^5\,\text{рад/с}q_{\text{м}}=5\cdot10^{-8}\,\text{Кл}I_{\text{м}}=0{,}03162\,\text{А}

Position in this set: 7 from 48

Problem #18

Electromagnetic vibrations

To a sinusoidal voltage network 220\,\text{В}, 50\,\text{Гц} resistor included 500\,\text{Ом}. Find the voltage and current amplitudes and cyclic frequency. The mains voltage is indicated as a rms value.

Answer options

  1. \left(155{,}5\,\text{В};\ 0{,}31\,\text{А};\ 157\,\text{рад/с}\right)
  2. \left(622\,\text{В};\ 1{,}24\,\text{А};\ 628\,\text{рад/с}\right)
  3. \left(3110\,\text{В};\ 6{,}2\,\text{А};\ 3140\,\text{рад/с}\right)
  4. \left(311\,\text{В};\ 0{,}62\,\text{А};\ 314\,\text{рад/с}\right)
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Given
U
220\,\text{В}
\nu
50\,\text{Гц}
R
500\,\text{Ом}
Find

U_{\text{м}}I_{\text{м}}\omega

  1. \omega = 2\pi\nu\omega = 2\cdot 3{,}14\cdot 50\omega = 314\,\tfrac{1}{\text{с}}
  2. U_{\text{м}} = U\sqrt{2}U_{\text{м}} = 220\cdot\sqrt{2}U_{\text{м}} = 311\,\text{В}

    The network indicates the effective voltage value.

  3. I_{\text{м}} = \dfrac{U_{\text{м}}}{R}I_{\text{м}} = \dfrac{311}{500}I_{\text{м}} = 0{,}62\,\text{А}

    Laws: u = 311 sin 314t (B), i = 0.62 sin 314t (A).

AnswerU_{\text{м}} = 311\,\text{В}I_{\text{м}} = 0{,}62\,\text{А}\omega = 314\,\tfrac{1}{\text{с}}

Position in this set: 8 from 48

Problem #19

Electromagnetic vibrations

To the network 220\,\text{В}, 50\,\text{Гц} turned on the capacitor 80\,\text{мкФ}. Determine the voltage and current amplitudes. What inductance must be connected in series for resonance? The mains voltage is indicated as a rms value.

Answer options

  1. \left(311\,\text{В};\ 7{,}8\,\text{А};\ 0{,}126\,\text{Гн}\right)
  2. \left(155{,}5\,\text{В};\ 3{,}9\,\text{А};\ 0{,}063\,\text{Гн}\right)
  3. \left(622\,\text{В};\ 15{,}6\,\text{А};\ 0{,}252\,\text{Гн}\right)
  4. \left(3110\,\text{В};\ 78\,\text{А};\ 1{,}26\,\text{Гн}\right)
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Given
C
80\,\text{мкФ}80\cdot 10^{-6}\,\text{Ф}
U
220\,\text{В}
\nu
50\,\text{Гц}
Find

U_{\text{м}}I_{\text{м}}L

  1. \omega = 2\pi\nu = 314\,\tfrac{1}{\text{с}},\quad U_{\text{м}} = U\sqrt{2}U_{\text{м}} = 220\sqrt{2}U_{\text{м}} = 311\,\text{В}
  2. X_C = \dfrac{1}{\omega C}X_C = \dfrac{1}{314\cdot 80\cdot 10^{-6}}X_C = 40\,\text{Ом}
  3. I_{\text{м}} = \dfrac{U_{\text{м}}}{X_C}I_{\text{м}} = \dfrac{311}{40}I_{\text{м}} = 7{,}8\,\text{А}
  4. X_C = X_L\ \Rightarrow\ \dfrac{1}{\omega C} = \omega L\ \Rightarrow\ L = \dfrac{1}{\omega^{2}C}L = \dfrac{1}{314^{2}\cdot 80\cdot 10^{-6}}L = 0{,}127\,\text{Гн}

    With such inductance, the reactances are equal and voltage resonance occurs.

AnswerU_{\text{м}} = 311\,\text{В}I_{\text{м}} = 7{,}8\,\text{А}L = 0{,}127\,\text{Гн}

Position in this set: 9 from 48

Problem #20

Electromagnetic vibrations

The capacitor was given a charge 4\cdot10^{-4}\,\text{Кл} and shorted it to the coil. Capacity 5\,\text{мкФ}, inductance 32\,\text{мГн}. Determine the cyclic frequency, voltage and current amplitudes. Neglect the loop resistance.

Answer options

  1. \left(25000\,\text{рад/с};\ 800\,\text{В};\ 10\,\text{А}\right)
  2. \left(2500\,\text{рад/с};\ 80\,\text{В};\ 1\,\text{А}\right)
  3. \left(1250\,\text{рад/с};\ 40\,\text{В};\ 0{,}5\,\text{А}\right)
  4. \left(5000\,\text{рад/с};\ 160\,\text{В};\ 2\,\text{А}\right)
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Given
q_{\text{м}}
4\cdot 10^{-4}\,\text{Кл}
C
5\,\text{мкФ}5\cdot 10^{-6}\,\text{Ф}
L
32\,\text{мГн}32\cdot 10^{-3}\,\text{Гн}
Find

\omegaU_{\text{м}}I_{\text{м}}

  1. \omega = \dfrac{1}{\sqrt{LC}}\omega = \dfrac{1}{\sqrt{32\cdot 10^{-3}\cdot 5\cdot 10^{-6}}}\omega = 2500\,\tfrac{1}{\text{с}}
  2. U_{\text{м}} = \dfrac{q_{\text{м}}}{C}U_{\text{м}} = \dfrac{4\cdot 10^{-4}}{5\cdot 10^{-6}}U_{\text{м}} = 80\,\text{В}
  3. I_{\text{м}} = q_{\text{м}}\omegaI_{\text{м}} = 4\cdot 10^{-4}\cdot 2500I_{\text{м}} = 1\,\text{А}

    Laws: q = 4·10⁻⁴ cos 2500t (C), u = 80 cos 2500t (B), i = cos(2500t + π/2) (A).

Answer\omega = 2500\,\tfrac{1}{\text{с}}U_{\text{м}} = 80\,\text{В}I_{\text{м}} = 1\,\text{А}

Position in this set: 10 from 48

Problem #21

Electromagnetic vibrations

In an oscillatory circuit, the frequency 2\cdot10^{5}\,\text{Гц}, inductance 1{,}5\,\text{мГн}, current amplitude 0{,}2\,\text{А}. Determine the capacitance and voltage amplitude.

Answer options

  1. \left(8{,}4 \cdot 10^{-10}\,\text{Ф};\ 756\,\text{В}\right)
  2. \left(4{,}2 \cdot 10^{-9}\,\text{Ф};\ 3780\,\text{В}\right)
  3. \left(4{,}2 \cdot 10^{-10}\,\text{Ф};\ 378\,\text{В}\right)
  4. \left(2{,}1 \cdot 10^{-10}\,\text{Ф};\ 189\,\text{В}\right)
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Given
\nu
2\cdot 10^{5}\,\text{Гц}
L
1{,}5\,\text{мГн}1{,}5\cdot 10^{-3}\,\text{Гн}
I_{\text{м}}
0{,}2\,\text{А}
Find

CU_{\text{м}}

  1. \nu = \dfrac{1}{2\pi\sqrt{LC}}\ \Rightarrow\ \nu^{2} = \dfrac{1}{4\pi^{2}LC}

    We expand Thomson's formula with respect to capacity.

  2. C = \dfrac{1}{4\pi^{2}L\nu^{2}}C = \dfrac{1}{4\cdot 3{,}14^{2}\cdot 1{,}5\cdot 10^{-3}\cdot\left(2\cdot 10^{5}\right)^{2}}C = 4{,}2\cdot 10^{-10}\,\text{Ф}
  3. \dfrac{CU_{\text{м}}^{2}}{2} = \dfrac{LI_{\text{м}}^{2}}{2}\ \Rightarrow\ U_{\text{м}} = I_{\text{м}}\sqrt{\dfrac{L}{C}}U_{\text{м}} = 0{,}2\sqrt{\dfrac{1{,}5\cdot 10^{-3}}{4{,}2\cdot 10^{-10}}}U_{\text{м}} = 378\,\text{В}

    The energy of the capacitor at maximum is equal to the energy of the coil at maximum.

AnswerC = 4{,}2\cdot 10^{-10}\,\text{Ф}U_{\text{м}} = 378\,\text{В}

Position in this set: 11 from 48

Problem #22

Electromagnetic vibrations

In AC circuit voltage 24\,\text{В} and frequency 200\,\text{Гц} capacitor is turned on. What is its capacity if the current is 0{,}8\,\text{А}?

Answer options

  1. 1{,}325 \cdot 10^{-5}\,\text{Ф}
  2. 5{,}3 \cdot 10^{-5}\,\text{Ф}
  3. 2{,}65 \cdot 10^{-4}\,\text{Ф}
  4. 2{,}65 \cdot 10^{-5}\,\text{Ф}
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Given
U
24\,\text{В}
\nu
200\,\text{Гц}
I
0{,}8\,\text{А}
Find

C

  1. X_C = \dfrac{U}{I}X_C = \dfrac{24\,\text{В}}{0{,}8\,\text{А}}X_C = 30\,\text{Ом}
  2. X_C = \dfrac{1}{2\pi\nu C}\ \Rightarrow\ C = \dfrac{1}{2\pi\nu X_C}C = \dfrac{1}{2\cdot 3{,}14\cdot 200\cdot 30}C = 2{,}65\cdot 10^{-5}\,\text{Ф}

AnswerC = 2{,}65\cdot 10^{-5}\,\text{Ф}

Position in this set: 12 from 48

Problem #23

Electromagnetic vibrations

In AC circuit voltage 12\,\text{В} and frequency 400\,\text{Гц} included steel conductor length 10\,\text{м} and cross section 0{,}6\,\text{мм}^{2}. Determine voltage and current amplitudes and cyclic frequency. The voltage is given as an effective value. Take the resistivity of steel equal to 0.12 Ohm mm²/m; neglect inductance.

Answer options

  1. \left(17\,\text{В};\ 8{,}5\,\text{А};\ 2512\,\text{рад/с}\right)
  2. \left(8{,}5\,\text{В};\ 4{,}25\,\text{А};\ 1256\,\text{рад/с}\right)
  3. \left(34\,\text{В};\ 17\,\text{А};\ 5024\,\text{рад/с}\right)
  4. \left(170\,\text{В};\ 85\,\text{А};\ 25120\,\text{рад/с}\right)
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Given
U
12\,\text{В}
\nu
400\,\text{Гц}
\ell
10\,\text{м}
S
0{,}6\,\text{мм}^{2}
\rho
0{,}12\,\tfrac{\text{Ом}\cdot\text{мм}^{2}}{\text{м}}
Find

U_{\text{м}}I_{\text{м}}\omega

  1. \omega = 2\pi\nu\omega = 2\cdot 3{,}14\cdot 400\omega = 2512\,\tfrac{1}{\text{с}}
  2. U_{\text{м}} = U\sqrt{2}U_{\text{м}} = 12\sqrt{2}U_{\text{м}} = 17\,\text{В}
  3. R = \dfrac{\rho\ell}{S}R = \dfrac{0{,}12\cdot 10}{0{,}6}R = 2\,\text{Ом}
  4. I_{\text{м}} = \dfrac{U_{\text{м}}}{R}I_{\text{м}} = \dfrac{17}{2}I_{\text{м}} = 8{,}5\,\text{А}

    Laws: u = 17 sin 2512t (V), i = 8.5 sin 2512t (A) - across the resistor, the current and voltage are in phase.

AnswerU_{\text{м}} = 17\,\text{В}I_{\text{м}} = 8{,}5\,\text{А}\omega = 2512\,\tfrac{1}{\text{с}}

Position in this set: 13 from 48

Problem #24

Electromagnetic vibrations

Coil inductor 0{,}03\,\text{Гн} included in the alternating current circuit. What is the frequency if at voltage 12\,\text{В} the current is 5\,\text{А}?

Answer options

  1. 127\,\text{Гц}
  2. 12{,}7\,\text{Гц}
  3. 6{,}35\,\text{Гц}
  4. 25{,}4\,\text{Гц}
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Given
L
0{,}03\,\text{Гн}
U
12\,\text{В}
I
5\,\text{А}
Find

\nu

  1. X_L = \dfrac{U}{I}X_L = \dfrac{12\,\text{В}}{5\,\text{А}}X_L = 2{,}4\,\text{Ом}
  2. X_L = 2\pi\nu L\ \Rightarrow\ \nu = \dfrac{X_L}{2\pi L}\nu = \dfrac{2{,}4}{2\cdot 3{,}14\cdot 0{,}03}\nu = 12{,}7\,\text{Гц}

Answer\nu = 12{,}7\,\text{Гц}

Position in this set: 14 from 48

Problem #25

Waves

For 5\,\text{с} mosquito wings make 2000 hesitation. Determine the frequency and period, as well as the length of the sound wave at speed 340\,\text{м/с}.

Answer options

  1. \left(800\,\text{Гц};\ 0{,}005\,\text{с};\ 1{,}7\,\text{м}\right)
  2. \left(4000\,\text{Гц};\ 0{,}025\,\text{с};\ 8{,}5\,\text{м}\right)
  3. \left(400\,\text{Гц};\ 0{,}0025\,\text{с};\ 0{,}85\,\text{м}\right)
  4. \left(200\,\text{Гц};\ 0{,}00125\,\text{с};\ 0{,}425\,\text{м}\right)
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Given
t
5\,\text{с}
n
2000
v
340\,\text{м/с}
Find

\nuT\lambda

  1. \nu = \dfrac{n}{t}\nu = \dfrac{2000}{5}\nu = 400\,\text{Гц}
  2. T = \dfrac{t}{n} = \dfrac{1}{\nu}T = \dfrac{5}{2000}T = 2{,}5\cdot 10^{-3}\,\text{с}
  3. v = \lambda\nu\ \Rightarrow\ \lambda = \dfrac{v}{\nu}\lambda = \dfrac{340}{400}\lambda = 0{,}85\,\text{м}

Answer\nu = 400\,\text{Гц}T = 2{,}5\cdot 10^{-3}\,\text{с}\lambda = 0{,}85\,\text{м}

Position in this set: 15 from 48

Problem #26

Waves

Period of oscillation in a wave 0{,}16\,\text{с}, wave speed 3\,\text{м/с}. Determine length, frequency and time 25 hesitation.

Answer options

  1. \left(0{,}24\,\text{м};\ 3{,}125\,\text{Гц};\ 2\,\text{с}\right)
  2. \left(0{,}96\,\text{м};\ 12{,}5\,\text{Гц};\ 8\,\text{с}\right)
  3. \left(4{,}8\,\text{м};\ 62{,}5\,\text{Гц};\ 40\,\text{с}\right)
  4. \left(0{,}48\,\text{м};\ 6{,}25\,\text{Гц};\ 4\,\text{с}\right)
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Given
T
0{,}16\,\text{с}
v
3\,\text{м/с}
n
25
Find

\lambda\nut

  1. v = \dfrac{\lambda}{T}\ \Rightarrow\ \lambda = vT\lambda = 3\cdot 0{,}16\lambda = 0{,}48\,\text{м}

    Wavelength is the path a wave travels in one period.

  2. \nu = \dfrac{1}{T}\nu = \dfrac{1}{0{,}16}\nu = 6{,}25\,\text{Гц}
  3. t = nTt = 25\cdot 0{,}16t = 4\,\text{с}

Answer\lambda = 0{,}48\,\text{м}\nu = 6{,}25\,\text{Гц}t = 4\,\text{с}

Position in this set: 16 from 48

Problem #27

Waves

During a lightning flash, a thunderstorm front moves directly towards the observer at a speed 20\,\text{м/с}. Thunder comes through 50\,\text{с} after the outbreak. Find the distance to the flash location and the time from the flash to the arrival of the front. Take the speed of sound relative to the ground to be equal to 340\,\text{м/с}, the time of light propagation is neglected.

Answer options

  1. \left(17000\,\text{м};\ 850\,\text{с}\right)
  2. \left(8500\,\text{м};\ 425\,\text{с}\right)
  3. \left(34000\,\text{м};\ 1700\,\text{с}\right)
  4. \left(1{,}7 \cdot 10^{5}\,\text{м};\ 8500\,\text{с}\right)
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Given
t
50\,\text{с}
v_{\text{з}}
340\,\text{м/с}
v_{\text{в}}
20\,\text{м/с}
Find

St_2

  1. S = v_{\text{з}}tS = 340\,\tfrac{\text{м}}{\text{с}}\cdot 50\,\text{с}S = 17\,000\,\text{м}

    The light arrives almost instantly, so the delay is the travel time of the sound.

  2. t_2 = \dfrac{S}{v_{\text{в}}}t_2 = \dfrac{17\,000}{20}850\,\text{с} \approx 14\,\text{мин}

AnswerS = 17\,000\,\text{м}t_2 = 850\,\text{с}

Position in this set: 17 from 48

Problem #28

Waves

Two common mode generators operate at a frequency 1{,}5\,\text{МГц}. What is the result of interference at the point for which the path difference 650\,\text{м}? The waves propagate in vacuum and have the same amplitudes A and the same polarization at the observation point.

Answer options

  1. \Delta r=6{,}5\lambda,\ A_{\text{рез}}=A
  2. \Delta r=3{,}25\lambda,\ A_{\text{рез}}=\sqrt2 A
  3. \Delta r=3\lambda,\ A_{\text{рез}}=2A
  4. \Delta r=3{,}5\lambda,\ A_{\text{рез}}=0
Show the walkthroughHide the walkthrough
Given
\nu
1{,}5\,\text{МГц}1{,}5\cdot 10^{6}\,\text{Гц}
\Delta d
650\,\text{м}
c
3\cdot 10^{8}\,\text{м/с}
Find

\Delta d/\lambdaA_{\text{рез}}

  1. \lambda = \dfrac{c}{\nu}\lambda = \dfrac{3\cdot 10^{8}}{1{,}5\cdot 10^{6}}200\,\text{м}\ \Rightarrow\ \dfrac{\lambda}{2} = 100\,\text{м}
  2. k=\dfrac{\Delta d}{\lambda/2}k=\dfrac{650}{100}k=6{,}5

    The number is not an integer: the path difference is not equal to either an integer number of wavelengths (maximum) or an odd number of half-wavelengths (minimum).

  3. \Delta\varphi=2\pi\dfrac{\Delta d}{\lambda}=6{,}5\pi

    The phase shift modulo 2π is equal to π/2.

  4. A_{\text{рез}}=\sqrt{A^2+A^2+2A^2\cos\Delta\varphi}A_{\text{рез}} = \sqrt{2}A

Answer\Delta d/\lambda=3{,}25A_{\text{рез}}=\sqrt{2}A

Position in this set: 18 from 48

Problem #29

Waves

Wavelength of the Krasnoyarsk radio station 1{,}5\,\text{км}. What is the frequency and how many oscillations occur per 0{,}2\,\text{мс}? What is the frequency of a sound wave with period 0{,}2\,\text{мс}?

Answer options

  1. \left(4 \cdot 10^{5}\,\text{Гц};\ 80\,\text{колебаний};\ 10000\,\text{Гц}\right)
  2. \left(2 \cdot 10^{6}\,\text{Гц};\ 400\,\text{колебаний};\ 50000\,\text{Гц}\right)
  3. \left(2 \cdot 10^{5}\,\text{Гц};\ 40\,\text{колебаний};\ 5000\,\text{Гц}\right)
  4. \left(1 \cdot 10^{5}\,\text{Гц};\ 20\,\text{колебаний};\ 2500\,\text{Гц}\right)
Show the walkthroughHide the walkthrough
Given
\lambda
1{,}5\,\text{км}1500\,\text{м}
\Delta t
0{,}2\cdot 10^{-3}\,\text{с}
T
0{,}2\cdot 10^{-3}\,\text{с}
c
3\cdot 10^{8}\,\text{м/с}
Find

\nun\nu_{\text{з}}

  1. \nu = \dfrac{c}{\lambda}\nu = \dfrac{3\cdot 10^{8}}{1500}\nu = 2\cdot 10^{5}\,\text{Гц}
  2. n = \nu\,\Delta tn = 2\cdot 10^{5}\cdot 0{,}2\cdot 10^{-3}n = 40
  3. \nu_{\text{з}} = \dfrac{1}{T}\nu_{\text{з}} = \dfrac{1}{0{,}2\cdot 10^{-3}}\nu_{\text{з}} = 5\cdot 10^{3}\,\text{Гц}

Answer\nu = 2\cdot 10^{5}\,\text{Гц}n = 40\nu_{\text{з}} = 5\cdot 10^{3}\,\text{Гц}

Position in this set: 19 from 48

Problem #30

Waves

Distance to plane 15\,\text{км}. How long does it take for an electromagnetic pulse to travel to the plane and back?

Answer options

  1. 5 \cdot 10^{-5}\,\text{с}
  2. 2 \cdot 10^{-4}\,\text{с}
  3. 0{,}001\,\text{с}
  4. 1 \cdot 10^{-4}\,\text{с}
Show the walkthroughHide the walkthrough
Given
R
15\,\text{км}15\,000\,\text{м}
c
3\cdot 10^{8}\,\text{м/с}
Find

t

  1. R = \dfrac{ct}{2}\ \Rightarrow\ t = \dfrac{2R}{c}t = \dfrac{2\cdot 15\,000}{3\cdot 10^{8}}t = 0{,}0001\,\text{с}

    The impulse travels the distance twice: back and forth.

Answert = 0{,}0001\,\text{с}

Position in this set: 20 from 48

Problem #31

Waves

The radar operates on a wave 6\,\text{см} and radiates 1250 pulses per second duration 4\,\text{мкс}. How many oscillations does a pulse contain and what is the longest reconnaissance range?

Answer options

  1. \left(20000\,\text{колебаний};\ 1{,}2 \cdot 10^{5}\,\text{м}\right)
  2. \left(10000\,\text{колебаний};\ 60000\,\text{м}\right)
  3. \left(40000\,\text{колебаний};\ 2{,}4 \cdot 10^{5}\,\text{м}\right)
  4. \left(2 \cdot 10^{5}\,\text{колебаний};\ 1{,}2 \cdot 10^{6}\,\text{м}\right)
Show the walkthroughHide the walkthrough
Given
\lambda
6\,\text{см}0{,}06\,\text{м}
\nu_{\text{и}}
1250\,\tfrac{1}{\text{с}}
\Delta t
4\,\text{мкс}4\cdot 10^{-6}\,\text{с}
c
3\cdot 10^{8}\,\text{м/с}
Find

nR_{\text{м}}

  1. \nu = \dfrac{c}{\lambda}\nu = \dfrac{3\cdot 10^{8}}{0{,}06}\nu = 5\cdot 10^{9}\,\text{Гц}
  2. n = \nu\,\Delta tn = 5\cdot 10^{9}\cdot 4\cdot 10^{-6}n = 20\,000

    So many oscillations fit into one impulse.

  3. R_{\text{м}} = \dfrac{cT_{\text{и}}}{2} = \dfrac{c}{2\nu_{\text{и}}}R_{\text{м}} = \dfrac{3\cdot 10^{8}}{2\cdot 1250}R_{\text{м}} = 120\,000\,\text{м} = 120\,\text{км}

Answern = 20\,000R_{\text{м}} = 120\,000\,\text{м}

Position in this set: 21 from 48

Problem #32

Waves

What wavelength is the receiver tuned to if the oscillating circuit has a capacitance 40\,\text{пФ} and inductance 22{,}5\,\text{мкГн}?

Answer options

  1. 565{,}2\,\text{м}
  2. 56{,}52\,\text{м}
  3. 28{,}26\,\text{м}
  4. 113{,}04\,\text{м}
Show the walkthroughHide the walkthrough
Given
C
40\,\text{пФ}40\cdot 10^{-12}\,\text{Ф}
L
22{,}5\,\text{мкГн}22{,}5\cdot 10^{-6}\,\text{Гн}
c
3\cdot 10^{8}\,\text{м/с}
Find

\lambda

  1. \lambda = cT = c\cdot 2\pi\sqrt{LC}\lambda = 3\cdot 10^{8}\cdot 2\cdot 3{,}14\sqrt{22{,}5\cdot 10^{-6}\cdot 40\cdot 10^{-12}}\lambda = 56{,}52\,\text{м}

Answer\lambda = 56{,}52\,\text{м}

Position in this set: 22 from 48

Problem #33

Waves

The distance between adjacent nodes of a standing electromagnetic wave 12\,\text{м}. What are the wavelength and frequency?

Answer options

  1. \left(48\,\text{м};\ 2{,}5 \cdot 10^{7}\,\text{Гц}\right)
  2. \left(240\,\text{м};\ 1{,}25 \cdot 10^{8}\,\text{Гц}\right)
  3. \left(24\,\text{м};\ 1{,}25 \cdot 10^{7}\,\text{Гц}\right)
  4. \left(12\,\text{м};\ 6{,}25 \cdot 10^{6}\,\text{Гц}\right)
Show the walkthroughHide the walkthrough
Given
S
12\,\text{м}
c
3\cdot 10^{8}\,\text{м/с}
Find

\lambda\nu

  1. S = \dfrac{\lambda}{2}\ \Rightarrow\ \lambda = 2S\lambda = 2\cdot 12\lambda = 24\,\text{м}

    Adjacent nodes of a standing wave are separated by half the wavelength.

  2. \nu = \dfrac{c}{\lambda}\nu = \dfrac{3\cdot 10^{8}}{24}\nu = 1{,}25\cdot 10^{7}\,\text{Гц}

Answer\lambda = 24\,\text{м}\nu = 1{,}25\cdot 10^{7}\,\text{Гц}

Position in this set: 23 from 48

Problem #34

Waves

For 20\,\text{с} the string commits 8000 hesitation. Speed of sound 340\,\text{м/с}. Find the frequency and wavelength. Which of the two obstacles, the size 0{,}2\,\text{м} or 20\,\text{м}, the bending of the sound wave will be more pronounced?

Answer options

  1. \left(400\,\text{Гц};\ 0{,}85\,\text{м};\ \text{у препятствия 20 м}\right)
  2. \left(400\,\text{Гц};\ 8{,}5\,\text{м};\ \text{у препятствия 0,2 м}\right)
  3. \left(40\,\text{Гц};\ 8{,}5\,\text{м};\ \text{у препятствия 20 м}\right)
  4. \left(400\,\text{Гц};\ 0{,}85\,\text{м};\ \text{у препятствия 0,2 м}\right)
Show the walkthroughHide the walkthrough
Given
t
20\,\text{с}
n
8000
v_{\text{з}}
340\,\text{м/с}
d_1
0{,}2\,\text{м}
d_2
20\,\text{м}
Find

\nu\lambda\text{obstacle with more expressed bending around}

  1. \nu = \dfrac{n}{t}\nu = \dfrac{8000}{20}\nu = 400\,\text{Гц}
  2. \lambda = \dfrac{v_{\text{з}}}{\nu}\lambda = \dfrac{340}{400}\lambda = 0{,}85\,\text{м}
  3. d_1<\lambda,\quad d_2\gg\lambda

    For an obstacle of 0.2 m, the bending is more pronounced, since its size is smaller than the wavelength. Behind an obstacle of 20 m, a more pronounced sound shadow is formed.

Answer\nu=400\,\text{Гц}\lambda=0{,}85\,\text{м}\text{Rounding stronger у obstacles 0,2 m}

Position in this set: 24 from 48

Problem #35

Waves

Two common-mode electromagnetic wave generators operate at a frequency 2{,}5\cdot10^{8}\,\text{Гц}. What is the result of interference at a point with a path difference 3\,\text{м}?

Answer options

  1. \Delta r=5\dfrac{\lambda}{2},\ \text{минимум}
  2. \Delta r=5\lambda,\ \text{максимум}
  3. \Delta r=2\lambda,\ \text{максимум}
  4. \Delta r=3\dfrac{\lambda}{2},\ \text{максимум}
Show the walkthroughHide the walkthrough
Given
\nu
2{,}5\cdot 10^{8}\,\text{Гц}
\Delta d
3\,\text{м}
c
3\cdot 10^{8}\,\text{м/с}
Find

\dfrac{\Delta d}{\lambda/2}

  1. \lambda = \dfrac{c}{\nu}\lambda = \dfrac{3\cdot 10^{8}}{2{,}5\cdot 10^{8}}1{,}2\,\text{м}\ \Rightarrow\ \dfrac{\lambda}{2} = 0{,}6\,\text{м}
  2. \dfrac{\Delta d}{\lambda/2}\dfrac{\Delta d}{\lambda/2} = \dfrac{3}{0{,}6}\dfrac{\Delta d}{\lambda/2} = 5

    An odd number of half-waves means there is a minimum at this point.

Answer\dfrac{\Delta d}{\lambda/2} = 5\ \text{- минимум}

Position in this set: 25 from 48

Problem #36

Waves

With what maximum frequency should radar pulses follow when reconnaissance of targets up to 150\,\text{км}?

Answer options

  1. 10000\,\text{Гц}
  2. 1000\,\text{Гц}
  3. 500\,\text{Гц}
  4. 2000\,\text{Гц}
Show the walkthroughHide the walkthrough
Given
R_{\text{м}}
150\,\text{км}150\cdot 10^{3}\,\text{м}
c
3\cdot 10^{8}\,\text{м/с}
Find

\nu_{\text{и}}

  1. R_{\text{м}} = \dfrac{cT_{\text{и}}}{2} = \dfrac{c}{2\nu_{\text{и}}}\ \Rightarrow\ \nu_{\text{и}} = \dfrac{c}{2R_{\text{м}}}\nu_{\text{и}} = \dfrac{3\cdot 10^{8}}{2\cdot 150\cdot 10^{3}}\nu_{\text{и}} = 1000\,\tfrac{1}{\text{с}}

    The next impulse cannot be sent before the previous one returns.

Answer\nu_{\text{и}} = 1000\,\text{Гц}

Position in this set: 26 from 48

Problem #39

Waves

What is one light year equal to?

Answer options

  1. 9{,}5 \cdot 10^{15}\,\text{м}
  2. 4{,}75 \cdot 10^{15}\,\text{м}
  3. 1{,}9 \cdot 10^{16}\,\text{м}
  4. 9{,}5 \cdot 10^{16}\,\text{м}
Show the walkthroughHide the walkthrough
Given
t
1\,\text{год}3{,}156\cdot 10^{7}\,\text{с}
c
3\cdot 10^{8}\,\text{м/с}
Find

S

  1. t = 365{,}25\cdot 24\cdot 3600t = 3{,}156\cdot 10^{7}\,\text{с}
  2. S = ctS = 3\cdot 10^{8}\cdot 3{,}156\cdot 10^{7}S = 9{,}5\cdot 10^{15}\,\text{м} = 9{,}5\cdot 10^{12}\,\text{км}

    A light year is a distance, not a time.

AnswerS = 9{,}5\cdot 10^{15}\,\text{м}

Position in this set: 27 from 48

Problem #40

Waves

How long does light take from the Sun to Pluto if the distance is 40\,\text{а.е.}?

Answer options

  1. 55{,}6\,\text{ч}
  2. 5{,}56\,\text{ч}
  3. 2{,}78\,\text{ч}
  4. 11{,}12\,\text{ч}
Show the walkthroughHide the walkthrough
Given
S
40\,\text{а.е.}6\cdot 10^{12}\,\text{м}
c
3\cdot 10^{8}\,\text{м/с}
Find

t

  1. S = ct\ \Rightarrow\ t = \dfrac{S}{c}t = \dfrac{6\cdot 10^{12}}{3\cdot 10^{8}}2\cdot 10^{4}\,\text{с} \approx 5{,}56\,\text{ч}

Answert = 5{,}56\,\text{ч}

Position in this set: 28 from 48

Problem #50

Waves

How do the wavelength, frequency and speed of monochromatic radiation change when passing from air to glass with n=1{,}5, if \lambda_{\text{возд}}=8\cdot10^{-7}\,\text{м}?

Answer options

  1. \left(2{,}665 \cdot 10^{-7}\,\text{м};\ 1{,}875 \cdot 10^{14}\,\text{Гц};\ 1 \cdot 10^{8}\,\text{м/с}\right)
  2. \left(1{,}066 \cdot 10^{-6}\,\text{м};\ 7{,}5 \cdot 10^{14}\,\text{Гц};\ 4 \cdot 10^{8}\,\text{м/с}\right)
  3. \left(5{,}33 \cdot 10^{-6}\,\text{м};\ 3{,}75 \cdot 10^{15}\,\text{Гц};\ 2 \cdot 10^{9}\,\text{м/с}\right)
  4. \left(5{,}33 \cdot 10^{-7}\,\text{м};\ 3{,}75 \cdot 10^{14}\,\text{Гц};\ 2 \cdot 10^{8}\,\text{м/с}\right)
Show the walkthroughHide the walkthrough
Given
n
1{,}5
\lambda
8\cdot 10^{-7}\,\text{м}
c
3\cdot 10^{8}\,\text{м/с}
Find

\lambda_{\text{ст}}\nuc_{\text{ст}}

  1. \lambda_{\text{ст}} = \dfrac{\lambda}{n}\lambda_{\text{ст}} = \dfrac{8\cdot 10^{-7}}{1{,}5}\lambda_{\text{ст}} = 5{,}33\cdot 10^{-7}\,\text{м}
  2. \nu = \dfrac{c}{\lambda}\nu = \dfrac{3\cdot 10^{8}}{8\cdot 10^{-7}}\nu = 3{,}75\cdot 10^{14}\,\text{Гц}

    The frequency is determined by the source and does not change when moving to another medium.

  3. c_{\text{ст}} = \dfrac{c}{n}c_{\text{ст}} = \dfrac{3\cdot 10^{8}}{1{,}5}c_{\text{ст}} = 2\cdot 10^{8}\,\tfrac{\text{м}}{\text{с}}

Answer\lambda_{\text{ст}} = 5{,}33\cdot 10^{-7}\,\text{м}\nu = 3{,}75\cdot 10^{14}\,\text{Гц}c_{\text{ст}} = 2\cdot 10^{8}\,\tfrac{\text{м}}{\text{с}}

Position in this set: 29 from 48

Problem #51

Waves

Wavelength of light in water 450\,\text{нм}. What is the frequency, wavelength in air and color of the rays? Accept n_{\text{воды}}=1{,}33.

Answer options

  1. \left(5\cdot10^{14}\,\text{Гц};\ 600\,\text{нм};\ \text{оранжевый}\right)
  2. \left(6{,}7\cdot10^{14}\,\text{Гц};\ 450\,\text{нм};\ \text{синий}\right)
  3. \left(5\cdot10^{14}\,\text{Гц};\ 338\,\text{нм};\ \text{ультрафиолет}\right)
  4. \left(3\cdot10^{8}\,\text{Гц};\ 600\,\text{нм};\ \text{красный}\right)
Show the walkthroughHide the walkthrough
Given
\lambda_{\text{в}}
450\,\text{нм}450\cdot 10^{-9}\,\text{м}
n_{\text{в}}
1{,}33
c
3\cdot 10^{8}\,\text{м/с}
Find

\nu\lambda\text{color}

  1. \lambda = \lambda_{\text{в}}n\lambda = 450\cdot 10^{-9}\cdot 1{,}33\lambda = 600\cdot 10^{-9}\,\text{м}

    The wave is longer in air than in water: it is orange light.

  2. \nu = \dfrac{c}{\lambda}\nu = \dfrac{3\cdot 10^{8}}{600\cdot 10^{-9}}\nu = 5\cdot 10^{14}\,\text{Гц}

Answer\nu=5\cdot10^{14}\,\text{Гц}\lambda=600\,\text{нм}\text{orange}

Position in this set: 30 from 48

Problem #53

Waves

Determine the frequency of radiation with wavelength 1{,}5\cdot10^{-7}\,\text{м}.

Answer options

  1. 4 \cdot 10^{15}\,\text{Гц}
  2. 2 \cdot 10^{16}\,\text{Гц}
  3. 2 \cdot 10^{15}\,\text{Гц}
  4. 1 \cdot 10^{15}\,\text{Гц}
Show the walkthroughHide the walkthrough
Given
\lambda
1{,}5\cdot 10^{-7}\,\text{м}
c
3\cdot 10^{8}\,\text{м/с}
Find

\nu

  1. \nu = \dfrac{c}{\lambda}\nu = \dfrac{3\cdot 10^{8}}{1{,}5\cdot 10^{-7}}\nu = 2\cdot 10^{15}\,\text{Гц}

    Frequency shows how many oscillations a wave makes per second.

Answer\nu = 2\cdot 10^{15}\,\text{Гц}

Position in this set: 31 from 48

Problem #104

Mechanical oscillations

For 30 with the pendulum committed 20 complete hesitation. Find the period.

Answer options

  1. 1{,}5\,\text{с}
  2. 3\,\text{с}
  3. 0{,}75\,\text{с}
  4. 4{,}5\,\text{с}
Show the walkthroughHide the walkthrough
Given
t
30\,\text{с}
N
20\,\text{колебаний}
Find

T

  1. T=\frac{t}{N}T=\frac{30}{20}T=1{,}5\,\text{с}

    A period is the time of one complete oscillation.

Answer1{,}5\,\text{с}

Position in this set: 32 from 48

Problem #105

Mechanical oscillations

For 40 with the pendulum committed 25 complete hesitation. Find the period.

Answer options

  1. 3{,}2\,\text{с}
  2. 1{,}6\,\text{с}
  3. 0{,}8\,\text{с}
  4. 4{,}8\,\text{с}
Show the walkthroughHide the walkthrough
Given
t
40\,\text{с}
N
25\,\text{колебаний}
Find

T

  1. T=\frac{t}{N}T=\frac{40}{25}T=1{,}6\,\text{с}

    A period is the time of one complete oscillation.

Answer1{,}6\,\text{с}

Position in this set: 33 from 48

Problem #106

Mechanical oscillations

Oscillation period 0{,}5 s. How many complete oscillations will occur in 2 min?

Answer options

  1. 480\,\text{колебаний}
  2. 240\,\text{колебаний}
  3. 120\,\text{колебаний}
  4. 720\,\text{колебаний}
Show the walkthroughHide the walkthrough
Given
T
0{,}5\,\text{с}
t
2\,\text{мин}
Find

N

  1. a=60ta=2 \cdot 60a=120\,\text{с}

    We reduce time to seconds.

  2. N=\frac{a}{T}N=\frac{120}{0{,}5}N=240\,\text{колебаний}

    We divide the total time into a period.

Answer240\,\text{колебаний}

Position in this set: 34 from 48

Problem #107

Mechanical oscillations

Oscillation period 0{,}8 s. How many complete oscillations will occur in 4 min?

Answer options

  1. 600\,\text{колебаний}
  2. 150\,\text{колебаний}
  3. 300\,\text{колебаний}
  4. 900\,\text{колебаний}
Show the walkthroughHide the walkthrough
Given
T
0{,}8\,\text{с}
t
4\,\text{мин}
Find

N

  1. a=60ta=4 \cdot 60a=240\,\text{с}

    We reduce time to seconds.

  2. N=\frac{a}{T}N=\frac{240}{0{,}8}N=300\,\text{колебаний}

    We divide the total time into a period.

Answer300\,\text{колебаний}

Position in this set: 35 from 48

Problem #108

Mechanical oscillations

Oscillation amplitude 5 cm, period 2 s. How far in meters will the point travel? 20 s? Time is equal to an integer number of periods.

Answer options

  1. 4\,\text{м}
  2. 1\,\text{м}
  3. 2\,\text{м}
  4. 6\,\text{м}
Show the walkthroughHide the walkthrough
Given
A
5\,\text{см}
T
2\,\text{с}
t
20\,\text{с}
Find

S

  1. N=\frac{t}{T}N=\frac{20}{2}N=10\,\text{колебаний}

    We determine the number of complete oscillations.

  2. a=\frac{A}{100}a=\frac{5}{100}a=0{,}05\,\text{м}

    Convert the amplitude to meters.

  3. S=4aNS=4 \cdot 0{,}05 \cdot 10S=2\,\text{м}

    During a period, a point passes through four amplitudes.

Answer2\,\text{м}

Position in this set: 36 from 48

Problem #109

Mechanical oscillations

Oscillation amplitude 8 cm, period 4 s. How far in meters will the point travel? 40 s? Time is equal to an integer number of periods.

Answer options

  1. 6{,}4\,\text{м}
  2. 1{,}6\,\text{м}
  3. 9{,}6\,\text{м}
  4. 3{,}2\,\text{м}
Show the walkthroughHide the walkthrough
Given
A
8\,\text{см}
T
4\,\text{с}
t
40\,\text{с}
Find

S

  1. N=\frac{t}{T}N=\frac{40}{4}N=10\,\text{колебаний}

    We determine the number of complete oscillations.

  2. a=\frac{A}{100}a=\frac{8}{100}a=0{,}08\,\text{м}

    Convert the amplitude to meters.

  3. S=4aNS=4 \cdot 0{,}08 \cdot 10S=3{,}2\,\text{м}

    During a period, a point passes through four amplitudes.

Answer3{,}2\,\text{м}

Position in this set: 37 from 48

Problem #110

Electromagnetic oscillations and alternating current

Oscillation frequency in the circuit 1000 Hz Find the period.

Answer options

  1. 0{,}002\,\text{с}
  2. 0{,}001\,\text{с}
  3. 0{,}0005\,\text{с}
  4. 0{,}003\,\text{с}
Show the walkthroughHide the walkthrough
Given
f
1000\,\text{Гц}
Find

T

  1. T=\frac{1}{f}T=\frac{1}{1000}T=0{,}001\,\text{с}

    Frequency and period are mutually inverse.

Answer0{,}001\,\text{с}

Position in this set: 38 from 48

Problem #111

Electromagnetic oscillations and alternating current

Oscillation frequency in the circuit 2000 Hz Find the period.

Answer options

  1. 0{,}001\,\text{с}
  2. 0{,}00025\,\text{с}
  3. 0{,}0005\,\text{с}
  4. 0{,}0015\,\text{с}
Show the walkthroughHide the walkthrough
Given
f
2000\,\text{Гц}
Find

T

  1. T=\frac{1}{f}T=\frac{1}{2000}T=0{,}0005\,\text{с}

    Frequency and period are mutually inverse.

Answer0{,}0005\,\text{с}

Position in this set: 39 from 48

Problem #112

Electromagnetic oscillations and alternating current

Coil inductance 20 mH, current 3 A. Find the energy of the magnetic field.

Answer options

  1. 0{,}18\,\text{Дж}
  2. 0{,}045\,\text{Дж}
  3. 0{,}09\,\text{Дж}
  4. 0{,}27\,\text{Дж}
Show the walkthroughHide the walkthrough
Given
L
20\,\text{мГн}
I
3\,\text{А}
Find

W

  1. l=L\cdot10^{-3}l=\frac{20}{1000}l=0{,}02\,\text{Гн}

    Convert millihenry to henry.

  2. W=\frac{lI^2}{2}W=\frac{0{,}02 \cdot {3}^{2}}{2}W=0{,}09\,\text{Дж}

    Energy depends on the square of the current.

Answer0{,}09\,\text{Дж}

Position in this set: 40 from 48

Problem #113

Electromagnetic oscillations and alternating current

Coil inductance 40 mH, current 2 A. Find the energy of the magnetic field.

Answer options

  1. 0{,}16\,\text{Дж}
  2. 0{,}04\,\text{Дж}
  3. 0{,}24\,\text{Дж}
  4. 0{,}08\,\text{Дж}
Show the walkthroughHide the walkthrough
Given
L
40\,\text{мГн}
I
2\,\text{А}
Find

W

  1. l=L\cdot10^{-3}l=\frac{40}{1000}l=0{,}04\,\text{Гн}

    Convert millihenry to henry.

  2. W=\frac{lI^2}{2}W=\frac{0{,}04 \cdot {2}^{2}}{2}W=0{,}08\,\text{Дж}

    Energy depends on the square of the current.

Answer0{,}08\,\text{Дж}

Position in this set: 41 from 48

Problem #114

Electromagnetic oscillations and alternating current

In an ideal circuit, a capacitor with a capacity 0{,}000004 F charged to 100 V, coil inductance 0{,}01 Mr. Find the maximum current.

Answer options

  1. 4\,\text{А}
  2. 1\,\text{А}
  3. 6\,\text{А}
  4. 2\,\text{А}
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Given
C
0{,}000004\,\text{Ф}
U
100\,\text{В}
L
0{,}01\,\text{Гн}
Find

I_{\max}

  1. W=\frac{CU^2}{2}W=\frac{0{,}000004 \cdot {100}^{2}}{2}W=0{,}02\,\text{Дж}

    At first, all the energy is in the electric field.

  2. I_{\max}^2=\frac{2W}{L}I_{\max}^2=\frac{2 \cdot 0{,}02}{0{,}01}I_{\max}^2=4\,\text{А}^{2}

    At maximum current, all the energy is in the magnetic field.

  3. I_{\max}=\sqrt{\frac{2W}{L}}I_{\max}=\sqrt{4}I_{\max}=2\,\text{А}

    In an ideal circuit, energy is conserved.

Answer2\,\text{А}

Position in this set: 42 from 48

Problem #115

Electromagnetic oscillations and alternating current

In an ideal circuit, a capacitor with a capacity 0{,}000009 F charged to 200 V, coil inductance 0{,}04 Mr. Find the maximum current.

Answer options

  1. 3\,\text{А}
  2. 6\,\text{А}
  3. 1{,}5\,\text{А}
  4. 9\,\text{А}
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Given
C
0{,}000009\,\text{Ф}
U
200\,\text{В}
L
0{,}04\,\text{Гн}
Find

I_{\max}

  1. W=\frac{CU^2}{2}W=\frac{0{,}000009 \cdot {200}^{2}}{2}W=0{,}18\,\text{Дж}

    At first, all the energy is in the electric field.

  2. I_{\max}^2=\frac{2W}{L}I_{\max}^2=\frac{2 \cdot 0{,}18}{0{,}04}I_{\max}^2=9\,\text{А}^{2}

    At maximum current, all the energy is in the magnetic field.

  3. I_{\max}=\sqrt{\frac{2W}{L}}I_{\max}=\sqrt{9}I_{\max}=3\,\text{А}

    In an ideal circuit, energy is conserved.

Answer3\,\text{А}

Position in this set: 43 from 48

Problem #116

Waves

Wave speed 12 m/s, frequency 3 Hz Find the wavelength.

Answer options

  1. 8\,\text{м}
  2. 2\,\text{м}
  3. 4\,\text{м}
  4. 12\,\text{м}
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Given
v
12\,\text{м/с}
f
3\,\text{Гц}
Find

\lambda

  1. \lambda=\frac{v}{f}\lambda=\frac{12}{3}\lambda=4\,\text{м}

    In one period, a wave travels one wavelength.

Answer4\,\text{м}

Position in this set: 44 from 48

Problem #117

Waves

Wave speed 20 m/s, frequency 5 Hz Find the wavelength.

Answer options

  1. 8\,\text{м}
  2. 2\,\text{м}
  3. 12\,\text{м}
  4. 4\,\text{м}
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Given
v
20\,\text{м/с}
f
5\,\text{Гц}
Find

\lambda

  1. \lambda=\frac{v}{f}\lambda=\frac{20}{5}\lambda=4\,\text{м}

    In one period, a wave travels one wavelength.

Answer4\,\text{м}

Position in this set: 45 from 48

Problem #118

Waves

Wavelength 0{,}5 m, for 10 with source committed 40 hesitation. Find the speed of the wave.

Answer options

  1. 4\,\text{м/с}
  2. 1\,\text{м/с}
  3. 6\,\text{м/с}
  4. 2\,\text{м/с}
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Given
l
0{,}5\,\text{м}
t
10\,\text{с}
N
40\,\text{колебаний}
Find

v

  1. f=\frac{N}{t}f=\frac{40}{10}f=4\,\text{Гц}

    Find the frequency of the source.

  2. v=\lambda fv=0{,}5 \cdot 4v=2\,\text{м/с}

    The frequency of the wave matches the frequency of the source.

Answer2\,\text{м/с}

Position in this set: 46 from 48

Problem #119

Waves

Wavelength 0{,}8 m, for 20 with source committed 50 hesitation. Find the speed of the wave.

Answer options

  1. 2\,\text{м/с}
  2. 4\,\text{м/с}
  3. 1\,\text{м/с}
  4. 6\,\text{м/с}
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Given
l
0{,}8\,\text{м}
t
20\,\text{с}
N
50\,\text{колебаний}
Find

v

  1. f=\frac{N}{t}f=\frac{50}{20}f=2{,}5\,\text{Гц}

    Find the frequency of the source.

  2. v=\lambda fv=0{,}8 \cdot 2{,}5v=2\,\text{м/с}

    The frequency of the wave matches the frequency of the source.

Answer2\,\text{м/с}

Position in this set: 47 from 48

Problem #120

Waves

In the first medium the wave speed 12 m/s, length 3 m. In the second environment the speed 8 m/s. How many wavelengths of the second medium fit at a distance 20 m? The frequency at the border does not change.

Answer options

  1. 10\,\text{длин волн}
  2. 20\,\text{длин волн}
  3. 5\,\text{длин волн}
  4. 30\,\text{длин волн}
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Given
v_1
12\,\text{м/с}
l_1
3\,\text{м}
v_2
8\,\text{м/с}
S
20\,\text{м}
Find

N

  1. f=\frac{v_1}{\lambda_1}f=\frac{12}{3}f=4\,\text{Гц}

    First we find a constant frequency.

  2. \lambda_2=\frac{v_2}{f}\lambda_2=\frac{8}{4}\lambda_2=2\,\text{м}

    In the second medium the wavelength changes.

  3. N=\frac{S}{\lambda_2}N=\frac{20}{2}N=10\,\text{длин волн}

    Divide the distance by the new wavelength.

Answer10\,\text{длин волн}

Position in this set: 48 from 48

Problem #121

Waves

In the first medium the wave speed 20 m/s, length 4 m. In the second environment the speed 10 m/s. How many wavelengths of the second medium fit at a distance 30 m? The frequency at the border does not change.

Answer options

  1. 30\,\text{длин волн}
  2. 15\,\text{длин волн}
  3. 7{,}5\,\text{длин волн}
  4. 45\,\text{длин волн}
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Given
v_1
20\,\text{м/с}
l_1
4\,\text{м}
v_2
10\,\text{м/с}
S
30\,\text{м}
Find

N

  1. f=\frac{v_1}{\lambda_1}f=\frac{20}{4}f=5\,\text{Гц}

    First we find a constant frequency.

  2. \lambda_2=\frac{v_2}{f}\lambda_2=\frac{10}{5}\lambda_2=2\,\text{м}

    In the second medium the wavelength changes.

  3. N=\frac{S}{\lambda_2}N=\frac{30}{2}N=15\,\text{длин волн}

    Divide the distance by the new wavelength.

Answer15\,\text{длин волн}

The theory behind these problems

Work through the topic if a problem will not give in.

Mechanical oscillationsPeriod, frequency, phase, velocity, acceleration and energy.Electromagnetic oscillations and alternating currentThe LC circuit, reactance and the transformer.WavesWavelength, speed, frequency, phase and reflected signals.

Formulas by topic

Look up symbols and units of measurement in the reference.

AmplitudeA, xₘ · мSpring constantk · Н/мPeriodT · сVelocityv · м/сFrequencyν · ГцAngular frequencyω · с⁻¹EnergyE, W · Дж