A commuter train blows its horn as it passes a passenger platform at a constant

Question

A commuter train blows its horn as it passes a passenger platform at a constant speed of 45.0 m/s. The train horn sounds at a frequency of 345 Hz when the train is at rest.

A commuter train blows its horn as it passes a passenger platform at a constant speed of 45.0 m/s. The train horn sounds at a frequency of 345 Hz when the train is at rest. (a) What is the frequency observed by a person on the platform as the train approaches? Hz (b) What is the frequency observed by a person on the platform as the train recedes from him? Hz (c) What wavelength does the observer find in each case? m m

Explanation / Answer

We will use doppler effect

speed of sound in air = c = 340m/s

a) when the train approches

F = f* (c + r)/c

where F= required freq

f=original freq

c=speed of sound in air = 340m/s

r=speed of approching train = 45m/s

F= 345*(340+45)/340 = 390.66Hz

B

F = f* (c - r) /c

F=345*(340-45)/340 = 299.33Hz

C)

we have wavelenght = speed/freq

so when approching wavelength = 340/390.66 = 0.87m

when receding = wavelength = 340/299.33 = 1.135m

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