Q: A church pipe is 0.25 m long. If both ends are open, what is the frequency of the first harmonic? (Speed of sound $$v = 343 m/s)$$

$$f_1$$ = \frac{343}{2 \times 0.25}$$ Hz

Question 1

Which of the following best describes the difference between transverse and longitudinal waves?

Accepted Answer

Transverse waves oscillate perpendicular to the direction of propagation, while longitudinal waves oscillate parallel.

Question 2

A wave traveling through a medium is described by $$y(x, t) = A \cos \left( \frac{2\pi}{\lambda} x - \frac{2\pi}{T} t \right). $$What is the physical meaning of $$\lambda in $$this equation?

Accepted Answer

$$\lambda is $$the wavelength, the distance between successive crests.

Question 3

If a wave pulse reflects from a fixed end, what happens to the reflected wave?

Accepted Answer

The reflected wave is inverted.

Question 4

When two waves of equal amplitude and frequency meet in phase, what type of interference occurs?

Accepted Answer

Constructive interference

Question 5

A standing wave is formed on a string fixed at both ends. What is the wavelength of the fundamental mode if the string length is $$L$$?

Accepted Answer

$$\lambda = 2L$$

Question 6

A church pipe is 0.25 m long. If both ends are open, what is the frequency of the first harmonic? (Speed of sound $$v = 343 m/s)$$

Accepted Answer

$$f_1$$ = \frac{343}{2 	imes 0.25}$$ Hz

Question 7

Which equation correctly relates the speed of a wave to its wavelength and frequency?

Accepted Answer

$$v = \lambda f$$

Question 8

If the path difference between two waves is $$n\lambda ($$where $$n is an $$integer), what type of interference occurs?

Accepted Answer

Constructive interference

Question 9

A sound source emits a frequency $$f$$ and moves towards a stationary observer with speed $$v_s. $$What is the observed frequency $$f'$$?

Accepted Answer

$$f' = f \frac{v}{v - v_s}$$

Question 10

Which of the following best explains why galaxies moving away from us appear redder?

Accepted Answer

Their light is red-shifted due to the Doppler effect.

Question 11

The intensity of sound at a distance $$r$$ from a point source is given by $$I = \frac{P}{4 \pi r^2$}. If $$the distance from the source is doubled, what happens to the intensity?

Accepted Answer

It becomes one-fourth as great.

Question 12

Two sound waves of frequencies 440 Hz and 444 Hz are played together. What is the beat frequency?

Accepted Answer

4 Hz

Question 13

A medical device uses the Doppler effect to measure blood flow. If the detector moves towards the source, what happens to the observed frequency?

Accepted Answer

It increases.

Question 14

The decibel level $$B of a $$sound is given by $$B = 10 \log \left( \frac{I}{I_0$} \right)$$, where $$I_0$$ = $$10^{-12} W/m$^2. If $$the intensity increases by a factor of 100, how much does the decibel level increase?

Accepted Answer

20 dB

Question 15

A wave pulse travels from a less dense medium to a more dense medium. How is the boundary treated and what happens to the reflected wave?

Accepted Answer

The boundary is treated as a fixed end and the wave is inverted.

Question 16

Which of the following is true about beats in sound?

Accepted Answer

Beats occur when two waves of slightly different frequencies interfere.

Question 17

For a pipe closed at one end and open at the other, what is the wavelength of the fundamental mode if the pipe length is $$L$$?

Accepted Answer

$$\lambda = 4L$$

Question 18

If two waves have a path difference of $$n \frac{\lambda}{2}$$, where $$n is $$odd, what type of interference occurs?

Accepted Answer

Destructive interference

Question 19

A tornado is detected using Doppler radar. What physical principle allows the radar to measure the tornado's speed?

Accepted Answer

Doppler shift in frequency of reflected waves

Waves and Sound: Principles, Interference, Standing Waves, and Doppler Effect

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