Standing at a crosswalk, you hear a frequency of 510 Hz from the siren of an approaching ambulance. After the ambulance passes, the observed frequency of the siren is 433 Hz. Determine the ambulance's speed from these observations. (Take the speed of sound to be 343 m/s.)

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Asked Nov 21, 2019
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Standing at a crosswalk, you hear a frequency of 510 Hz from the siren of an approaching ambulance. After the ambulance passes, the observed frequency of the siren is 433 Hz. Determine the ambulance's speed from these observations. (Take the speed of sound to be 343 m/s.)

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Expert Answer

Step 1

Apparent frequency is given by

v+v
v-y
f =v,
-fo
fisthe apparent frequency, visthevelocity ofsoundin air
v, is thevelocity of thereceiver
vis the vel ocity of the source and f, is theactual frequency
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v+v v-y f =v, -fo fisthe apparent frequency, visthevelocity ofsoundin air v, is thevelocity of thereceiver vis the vel ocity of the source and f, is theactual frequency

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Step 2

Velocity of the source can have two signs. If the source is moving away, the speed of source will have +sign. For approaching source, speed will have –sign.

Then for the observed frequency 510Hz,

343m/s+0
f(1)
343m/s-v
510HZ
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343m/s+0 f(1) 343m/s-v 510HZ

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Step 3

For the observed fre...

343m/s+0
fo (2)
433HZ
343m/s+v
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343m/s+0 fo (2) 433HZ 343m/s+v

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