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For a source producing a 1260 Hz tone, calculate the tone heard by a listener for the following separate cases, assuming a speed of sound cg = 344 m/s: a) The listener and source both travel toward each other at 43 m/s (note: this is cs). b) The listener is at rest, and the source approaches them at 86 m/s. c) The source is at rest, and the listener approaches them at 86 m/s. d) The listener flees from the source at 43 m/s, but the source is chasing them down at 129 m/s. e) The source flees from the listener at 43 m/s, but the listener is chasing them down at 129 m/s. f) In all of these cases the relative velocity of the source and listener is 86 m/s. Why then does the listener hear a different tone for each?

For a source producing a 1260 Hz tone, calculate the tone heard by a listener for the following separate cases, assuming a speed of sound cg = 344 m/s: a) The listener and source both travel toward each other at 43 m/s (note: this is cs). b) The listener is at rest, and the source approaches them at 86 m/s. c) The source is at rest, and the listener approaches them at 86 m/s. d) The listener flees from the source at 43 m/s, but the source is chasing them down at 129 m/s. e) The source flees from the listener at 43 m/s, but the listener is chasing them down at 129 m/s. f) In all of these cases the relative velocity of the source and listener is 86 m/s. Why then does the listener hear a different tone for each?

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For a source producing a 1260 Hz tone, calculate the tone heard by a listener for the following separate cases, assuming a speed of sound cs = 344 m/s: a) The listener and source both travel toward each other at 43 m/s (note: this is cs). b) The listener is at rest, and the source approaches them at 86 m/s. c) The source is at rest, and the listener approaches them at 86 m/s. d) The listener flees from the source at 43 m/s, but the source is chasing them down at 129 m/s. e) The source flees from the listener at 43 m/s, but the listener is chasing them down at 129 m/s. f) In all of these cases the relative velocity of the source and listener is 86 m/s. Why then does the listener hear a different tone for each?
Transcribed Image Text:For a source producing a 1260 Hz tone, calculate the tone heard by a listener for the following separate cases, assuming a speed of sound cs = 344 m/s: a) The listener and source both travel toward each other at 43 m/s (note: this is cs). b) The listener is at rest, and the source approaches them at 86 m/s. c) The source is at rest, and the listener approaches them at 86 m/s. d) The listener flees from the source at 43 m/s, but the source is chasing them down at 129 m/s. e) The source flees from the listener at 43 m/s, but the listener is chasing them down at 129 m/s. f) In all of these cases the relative velocity of the source and listener is 86 m/s. Why then does the listener hear a different tone for each?
Expert Solution
Step 1

Given that

frequency of source,f0=1260 Hz

Speed of soundcs=344 m/s

According to doppler effect,we have

f'=f0cs±vrcs±vs

(a)

The listener and source both travel toward each other at 43 m/s.

Here velocity of the listener,vr=43+43=86 m/s

velocity of the source,vs=43 m/s

then the tone heard by the listener

f'=f0cs+vrcs+vs=1260344+86344+43=1386.3 Hz

(b)

The listener is at rest and the source approaches them at 86 m/s.

Here velocity of the listener,vr=0

velocity of the source,vs=86 m/s

then the tone heard by the listener

f'=f0cs+vrcs-vs=1260344+0344-86=2265 Hz

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Follow-up Question

Wouldn't be equate to 1680 Hz after computation, not 2265 Hz?

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