Question

7. You are standing still on a day when there is no wind. Four different sources of sound are moving relative to you (either directly toward you or directly away from you). State whether each source is moving toward you or away from you and state how rapidly (in m/s) it is moving relative to you. The speed of sound in air is 343 m/s. Explain your answers. (a) Source 1 emits sound of frequency 125 Hz, but the sound you hear has frequency 135 Hz. (b) Source 2 emits sound of frequency 475 Hz, but the sound you hear has frequency 465 Hz. 8. In the above questions, if the sources are stationary and you (listener) are moving, find out whether you are moving toward or away from the sound source and your speed if: (a) Source 1 emits sound of frequency 125 Hz, but the sound you hear has frequency 135 Hz. (b) Source 2 emits sound of frequency 475 Hz, but the sound you hear has frequency 465 Hz.

Answer 1

7.Let velocity of sound be v=343 m/s, original frequency be f₀ and observed frequency be f.

a)If source is moving towards the observer with velocity u m/s, and observer is at rest,then observed frequency is given by:

f=v/(v-u)*f₀ and observed frequency is more than the original frequency. In the given problem, observed frequency is more than original frequency, so source is moving towards the observer.

f=135 Hz, f₀=125 Hz, v=343 m/s.

135=343/(343-u)*125=>135(343-u)=343*125=>46305-135u=42875=>135u=3430=>u=25.41 m/s

b)If source is moving away from the observer with velocity u m/s, and observer is at rest,then observed frequency is given by:f=v/(v+u)*f₀, and observed frequency is less than the original frequency.In the given problem, observed frequency is less than original frequency, so source is moving away from the observer.

f=465 Hz,f₀=475 Hz,v=343m/s

465=343/(343+u)*475=>465(343+u)=343*475=>159495+465u=162925=>465u=3430=>u=7.38 m/s

8..Let velocity of sound be v=343 m/s, original frequency be f₀ and observed frequency be f.

a)If source is stationary, and observer is moving towards the source with velocity u m/s, then observed frequency is given by

f=(v+u)/v*f₀ and observed frequency is more than the original frequency. In the given problem, observed frequency is more than original frequency, so observer is moving towards the source.

f=135 Hz, f₀=125 Hz, v=343 m/s.

135=125*(343+u)/343=>343*135=125(343+u)=>46305=42875+125u=>3430=125u=>u=27.44 m/s

b)

)If source is stationary, and observer is moving away from the source with velocity u m/s, then observed frequency is given by

f=(v-u)/v*f₀ and observed frequency is less than the original frequency. In the given problem, observed frequency is less than original frequency, so observer is moving away from the source.

f=465 Hz,f₀=475 Hz,v=343m/s

465=475*(343-u)/343=>465*343=475(343-u)=>159495=162925-475u=>3430=475u=>u=7.22 m/s