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Question
The sound emitted from the siren of an ambulance has a frequency of 1500 Hz. The speed of sound is 340 m/s. Calculate the difference in frequencies heard by a stationary observer if the ambulance initially travels towards and then away from the observer at a speed of 30 m/s.
Solution
Given: vs = 30 m/s, n0 = 1500 Hz, v = 340 m/s
To find: Difference in apparent frequencies (nA − n'A)
Formulae:
- When the ambulance moves towards the stationary observer, then `"n"_"A" = "n"_0("v"/("v" - "v"_"s"))`
- When the ambulance moves away from the stationary observer, then `"n"'_"A" = "n"_0("v"/("v" + "v"_"s"))`
Calculation: From formula (i),
`"n"_"A" = 1500(3400/(340 − 30))`
∴ nA = 1645 Hz
From formula (ii),
n'A = 1500`(340/(340 + 30))`
∴ n'A = 1378 Hz
Difference between nA and n'A
= nA − n'A = 1645 − 1378 = 267 Hz
The difference in frequencies heard by the stationary observer is 267 Hz.
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