A passenger train approaching a station at a speed of 90 mph blows a whistle of

Question

A passenger train approaching a station at a speed of 90 mph blows a whistle of frequency 500 Hz. The frequency of the whistle as heard by a passenger riding in the last car of the train is _____. The frequency of the whistle as heard by a person standing in the station is _____. The frequency of the whistle as heard by a passenger on another train behind the first train traveling in the same direction at 80 mph is _____. The frequency o whistle as heard by a on another train traveling towards the first train from the opposite direction at 80 mph is _____. A string of linear density 2 times 10^2 kg/m is stretched to a tension of 50 N. The speed of a wave propagating in this string is _____. The wavelength of the sound wave created by a tuning fork of frequency 500 Hz is _____.

Explanation / Answer

1 According to Doppler Effect apparent frequency n' = n (V--Vo) / V--Vs). Since passenger is travelling in the same train So his speed Vo = speed of train Vs .So from the above expression, n' = n =500 hz only.so frequency heard by the passenger remains the same. Apparent frequency does not depend on length of train

2 from Doppler effect formula Vo= 0 since person or observer is stationary. Substituting the values Velocity of sound V=330 m/s, Velocity of source(train) Vs= 40 m/s(90 mph=90*1.6 *5/18) , n=500 Hz , n' = 569 m/s

3 In the above formula substituting Vs=40 m/s,V =330 m/s,n=500 Hz and Vo =speed of passenger= speed of second train = 36 m/s (80*1.6*5/18) we get n'=n(V-Vo) / V-Vs =506.89 m/s =507 m/s

4 When train or source of sound travelling in opposite direction to an another train(in which passenger is present) Vo is taken as negative :' n' = n(V+Vo) / V-Vs = 500(330+36) / 290 = 631 m/s

5 Velocity of sound in a stretched wire is given by V = Square root of T/M ie, T= tension in the string and mue(M) is linear density root of 50/2*100 = 50 m/s

6 Fro the formula V =n X , X lamda (wave length of sound )=V/n =330/500 =0.66 =0.7 m

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