Q: A sound source emits a frequency $$f_s = 500\ \mathrm{Hz}$$ and moves away from a stationary observer at $$v_s = 30\ \mathrm{m/s}. $$The speed of sound is $$v = 340\ \mathrm{m/s}. $$What frequency does the observer hear?

$$f_o = 500 \times \dfrac{340}{340 + 30} = 459\ \mathrm{Hz}$$

Q: A stationary source emits a sound at $$f_s = 600\ \mathrm{Hz}. An $$observer moves toward the source at $$v_o = 20\ \mathrm{m/s}$$, with the speed of sound $$v = 340\ \mathrm{m/s}. $$What frequency does the observer hear?

$$f_o = 600 \times \dfrac{340 + 20}{340} = 635\ \mathrm{Hz}$$

Q: A train is moving away from you at $$v_s = 40\ \mathrm{m/s}$$, blowing a whistle at $$f_s = 500\ \mathrm{Hz}. $$The speed of sound is $$v = 340\ \mathrm{m/s}. $$What frequency do you hear?

$$f_o = 500 \times \dfrac{340}{340 + 40} = 446\ \mathrm{Hz}$$

Question 1

Two sound waves with frequencies $$f_1 = 440$$\ \mathrm{Hz}$$ and f_2$ = 444\ \mathrm{Hz}$$ are played together. What is the beat frequency heard by an observer?

Accepted Answer

$$4\ \mathrm{Hz}$$

Question 2

A stationary observer hears the frequency of a siren from an ambulance moving toward them at speed $$v_s. $$The speed of sound is $$v. $$What is the observed frequency $$f_o if $$the source frequency is $$f_s$$?

Accepted Answer

$$f_o = \dfrac{v}{v - v_s} f_s$$

Question 3

A sound source emits a frequency $$f_s = 500\ \mathrm{Hz}$$ and moves away from a stationary observer at $$v_s = 30\ \mathrm{m/s}. $$The speed of sound is $$v = 340\ \mathrm{m/s}. $$What frequency does the observer hear?

Accepted Answer

$$f_o = 500 	imes \dfrac{340}{340 + 30} = 459\ \mathrm{Hz}$$

Question 4

You hear a sound with a frequency of $$256\ \mathrm{Hz}. $$The amplitude increases and decreases periodically, taking $$2\ \mathrm{s} to go $$from loud to soft and back to loud. What are the frequencies of the two waves producing this beat?

Accepted Answer

$$255.75\ \mathrm{Hz}$$ and $$256.25\ \mathrm{Hz}$$

Question 5

Which of the following best describes what happens to the frequency and wavelength of a sound as a source moves toward a stationary observer?

Accepted Answer

The observer hears a higher frequency and a shorter wavelength.

Question 6

A police car with its siren on is moving toward a stationary observer. Which equation gives the observed frequency $$f_o$$?

Accepted Answer

$$f_o = \dfrac{v}{v - v_s} f_s$$

Question 7

A stationary source emits a sound at $$f_s = 600\ \mathrm{Hz}. An $$observer moves toward the source at $$v_o = 20\ \mathrm{m/s}$$, with the speed of sound $$v = 340\ \mathrm{m/s}. $$What frequency does the observer hear?

Accepted Answer

$$f_o = 600 	imes \dfrac{340 + 20}{340} = 635\ \mathrm{Hz}$$

Question 8

Which of the following is a real-world application of the Doppler Effect?

Accepted Answer

Measuring the speed of blood flow in the heart using ultrasound.

Question 9

If both the observer and the source are moving toward each other, which equation gives the observed frequency $$f_o$$?

Accepted Answer

$$f_o = \dfrac{v + v_o}{v - v_s} f_s$$

Question 10

A train is moving away from you at $$v_s = 40\ \mathrm{m/s}$$, blowing a whistle at $$f_s = 500\ \mathrm{Hz}. $$The speed of sound is $$v = 340\ \mathrm{m/s}. $$What frequency do you hear?

Accepted Answer

$$f_o = 500 	imes \dfrac{340}{340 + 40} = 446\ \mathrm{Hz}$$

Question 11

Which of the following statements about beats is correct?

Accepted Answer

Beats occur when two waves of slightly different frequencies interfere, causing periodic variations in amplitude.

Question 12

A sound wave travels at $$v = 340\ \mathrm{m/s}$$ and has a frequency of $$f = 170\ \mathrm{Hz}. $$What is its wavelength?

Accepted Answer

$$\lambda = \dfrac{340}{170} = 2\ \mathrm{m}$$

Question 13

A stationary observer hears a frequency $$f_o$$ from a source moving away at speed $$v_s. $$Which of the following is true?

Accepted Answer

$$f_o \u003c f_s$$

Question 14

Which of the following best describes the Doppler Effect with light as observed in astronomy?

Accepted Answer

It is used to determine the motion of stars and galaxies relative to Earth by measuring shifts in spectral lines.

Question 15

If a sound source and observer are both stationary, but the wind blows from the source toward the observer, what happens to the observed frequency?

Accepted Answer

The observed frequency remains unchanged.

Question 16

A medical ultrasound device uses the Doppler Effect to measure blood flow. If blood is moving toward the probe, what happens to the frequency of the reflected sound?

Accepted Answer

The frequency increases.

Question 17

Which equation correctly gives the beat frequency when two waves of frequencies $$f_1$$ and $$f_2$$ are played together?

Accepted Answer

$$f_{\mathrm{beat}} = |f_1$ - f_2$|$$

Question 18

A car is moving toward a stationary observer at $$v_o = 20\ \mathrm{m/s}$$, emitting a sound at $$f_s = 400\ \mathrm{Hz}. $$The speed of sound is $$v = 340\ \mathrm{m/s}. $$What frequency does the observer hear?

Accepted Answer

$$f_o = 400 	imes \dfrac{340 + 20}{340} = 423.5\ \mathrm{Hz}$$

Question 19

Which of the following is NOT a necessary condition for the Doppler Effect to occur?

Accepted Answer

The observer must be stationary.

Waves, Beats, and the Doppler Effect: Study Notes

Study Guide - Practice Questions

Study Guide - Flashcards