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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Question

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, $f_{0} = 1260 H z$

Speed of sound $c_{s} = 344 m / s$

According to doppler effect,we have

$f' = f_{0} (\frac{c_{s} \pm v_{r}}{c_{s} \pm v_{s}})$

(a)

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

Here velocity of the listener, $v_{r} = 43 + 43 = 86 m / s$

velocity of the source, $v_{s} = 43 m / s$

then the tone heard by the listener

$f' = f_{0} [\frac{c_{s} + v_{r}}{c_{s} + v_{s}}] = 1260 [\frac{344 + 86}{344 + 43}] = 1386.3 H z$

(b)

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

Here velocity of the listener, $v_{r} = 0$

velocity of the source, $v_{s} = 86 m / s$

then the tone heard by the listener

$f' = f_{0} [\frac{c_{s} + v_{r}}{c_{s} - v_{s}}] = 1260 [\frac{344 + 0}{344 - 86}] = 2265 H z$

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Follow-up Question

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

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