Practice Resonance in Physics

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

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Quick Recap

Resonance occurs when a system is driven at or near one of its natural frequencies, causing the amplitude of its oscillation to grow strongly.

Push at just the right rhythm and the vibration builds up much more than usual.

Showing a random 20 of 50 problems.

Example 1

medium

An open tube of length

0.4\text{ m}

(v =

320\text{ m/s}

) resonates at fundamental. Find the frequency.

Example 2

challenge

A closed tube of length

L = 0.34\text{ m}

resonates at fundamental. With

v = 340\text{ m/s}

, find the next two resonant frequencies above the fundamental.

Example 3

hard

A spring-mass system has

f_0 = 4\text{ Hz}

. The spring constant is quadrupled. Find the new resonant frequency.

Example 4

medium

A child on a swing of natural period 2 s is pushed every 2 s and the amplitude grows. If the pushing period changed to 1 s, would resonance still occur?

Example 5

medium

An open tube of length 0.5 m (v = 340 m/s) resonates at its fundamental. What driving sound frequency causes this resonance? (

f = \frac{v}{2L}

Example 6

challenge

A circuit has natural (resonant) frequency

f_0 = 1/(2\pi\sqrt{LC})

with

L = 1.0\text{ mH}

and

C = 10\text{ nF}

. Find

f_0

Example 7

easy

A tuning fork at

256\text{ Hz}

resonates with an air column. The column resonates because its natural frequency matches what?

Example 8

easy

A closed (one-end-closed) tube of length

0.5\text{ m}

resonates fundamentally when

L = \lambda/4

. Find the wavelength.

Example 9

medium

A driven oscillator's amplitude is highest at

f = 50\text{ Hz}

. What is the system's natural frequency?

Example 10

easy

Resonance occurs when a system is driven at which frequency?

Example 11

hard

A pendulum has

L = 0.25\text{ m}

and

g = 9.8\text{ m/s}^2

. Find the resonant driving frequency.

Example 12

challenge

A closed resonance tube first resonates at 0.18 m and next at 0.55 m for a fork. Find the speed of sound if the fork is 460 Hz. (Use the half-wavelength difference.)

Example 13

medium

A mass on a spring has natural frequency

f_0 = \frac{1}{2\pi}\sqrt{\frac{k}{m}}

. With

k = 200

N/m and

m = 0.5

kg, find the driving frequency for resonance.

Example 14

medium

A closed tube resonates fundamentally at

850\text{ Hz}

with

v = 340\text{ m/s}

. Find the tube length.

Example 15

challenge

An open pipe (v = 340 m/s) must resonate at exactly 850 Hz in its fundamental. What length should it be? (

f_1 = \frac{v}{2L}

Example 16

easy

What limits how large the amplitude grows at resonance?

Example 17

easy

A pendulum's natural frequency is 0.5 Hz. To resonate it, at what frequency should you push?

Example 18

medium

A bridge has a natural frequency of 2 Hz. Soldiers march across at 2 steps per second. Why is this dangerous?

Example 19

easy

Resonance produces the largest amplitude when driving frequency equals what frequency of the system?

Example 20

medium

A closed tube has

L = 0.25\text{ m}

. With

v = 340\text{ m/s}

, find the fundamental resonant frequency.

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