Q: If two sound waves of frequencies $$f_1 = 500$$\ \mathrm{Hz}$$ and f_2$ = 505\ \mathrm{Hz}$$ are played together, what is the beat frequency heard?

$$f_{\text{beat}} = 5\ \mathrm{Hz}$$

Question 1

Two wave pulses are approaching each other on a string as shown in the first image. Each pulse travels at $$1\ \mathrm{m/s}. At$$ $$t = 2\ \mathrm{s}$$, what will be the displacement at $$x = 4\ \mathrm{m}$$?

Accepted Answer

The displacement will be the sum of the displacements of both pulses at that point, according to the principle of superposition.

Question 2

Refer to the second image. What is the mode number $$m of $$the standing wave shown on the string fixed at both ends?

Accepted Answer

$$m = 5$$

Question 3

For a standing wave on a string fixed at both ends, what is the distance between two adjacent nodes?

Accepted Answer

$$\frac{1}{2} \lambda$$

Question 4

A 170 Hz sound wave in air has a wavelength of 2.0 m. If the frequency is doubled to 340 Hz, what is the new wavelength? (Speed of sound in air is 343 m/s.)

Accepted Answer

1.0 m

Question 5

In the fifth image, which locations on the string are nodes?

Accepted Answer

Points of zero amplitude

Question 6

For the standing wave shown in the sixth image, what is the wavelength?

Accepted Answer

2.0 m

Question 7

Which tube in the seventh image will have the lowest fundamental frequency for standing sound waves?

Accepted Answer

Tube C (open at one end, closed at the other)

Question 8

In the eighth image, what type of interference occurs at point Q?

Accepted Answer

Destructive interference

Question 9

If two sound waves of frequencies $$f_1 = 500$$\ \mathrm{Hz}$$ and f_2$ = 505\ \mathrm{Hz}$$ are played together, what is the beat frequency heard?

Accepted Answer

$$f_{	ext{beat}} = 5\ \mathrm{Hz}$$

Question 10

A 2.5-m-long string with a mass of 0.10 kg is fixed at both ends and under a tension of 30 N. What is the speed $$v of $$waves on the string?

Accepted Answer

$$v = \sqrt{\frac{T}{\mu}} = \sqrt{\frac{30}{0.04}} = 27.4\ \mathrm{m/s}$$

Question 11

A string fixed at both ends is 3.0 m long and resonates in its second harmonic at a frequency of 60 Hz. What is the speed of the wave on the string?

Accepted Answer

$$v = 120\ \mathrm{m/s}$$

Question 12

For a tube open at one end and closed at the other, which harmonics are supported?

Accepted Answer

Only odd harmonics (1, 3, 5, ...)

Question 13

If two speakers are 3.0 m apart and emit sound at 170 Hz, and Sam stands 4.0 m in front of one speaker, what is the path difference between the two speakers to Sam?

Accepted Answer

$$1.0\ \mathrm{m}$$

Question 14

A bat emits a sound at $$f_1 = 40$$\ \mathrm{kHz}$$, and a detector mixes this with a tunable oscillator at f_2$ = 39.995\ \mathrm{kHz}. $$What frequency will be heard from the speaker after filtering?

Accepted Answer

$$0.005\ \mathrm{kHz}$$

Question 15

For a standing wave on a string of length $$L$$ fixed at both ends, what is the wavelength of the $$nth $$harmonic?

Accepted Answer

$$\lambda_n = \frac{2L}{n}$$

Question 16

What is the frequency of the third harmonic for a string of length $$L$$ and wave speed $$v$$ fixed at both ends?

Accepted Answer

$$f_3$$ = \frac{3v}{2L}$$

Question 17

If the path difference between two sound sources at a point is $$\Delta r = (m + \frac{1}{2})\lambda$$, what type of interference occurs at that point?

Accepted Answer

Destructive interference

Question 18

A tube open at one end and closed at the other has a length $$L = 0.5175\ \mathrm{m}. If $$the speed of sound is $$v = 345\ \mathrm{m/s}$$, what is the fundamental frequency?

Accepted Answer

$$f_1$$ = \frac{v}{4L}$$

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