A commuter train blows its horn as it passes a passenger platformat a constant s

Question

A commuter train blows its horn as it passes a passenger platformat a constant speed of 30.0 m/s. The trainhorn sounds at a frequency of 330 Hz whenthe train is at rest. (a) What is the frequency observed by a personon the platform as the train approaches?
1 Hz

(b) What is the frequency observed by a person on the platform asthe train recedes from him?
2 Hz

(c) What wavelength does the observer find in each case?
3 m
4 m (a) What is the frequency observed by a personon the platform as the train approaches?
1 Hz

(b) What is the frequency observed by a person on the platform asthe train recedes from him?
2 Hz

(c) What wavelength does the observer find in each case?
3 m
4 m

Explanation / Answer

Speed of train v = 30 m / s Frequency of sound f = 330 Hz (a).  Let the frequency observed by a person on theplatform as the train approaches be f ' then f ' = [ v / ( v - v ' ) ] f where v= speed of sound = 344 m / s plug the values weget f ' = 361.52 Hz (b). Let the frequency observed by a person on theplatform as the train recedes from him be f " then f " = [ v / ( v + v ' ) ] f             =303.52 Hz (c). wavelengths   ' = v / f '                               = 0.9515 m wavelength in case ( 2 ) is " = v / f "                                             = 1.13333 m

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