Suppose a train that has a 150-Hz horn is moving at 35.0 m/s in still air on a day when the speed of sound is 340 m/s. (a) What frequencies are observed by a stationary person at the side of the tracks as the train approaches and after it passes? (b) What frequency is observed by the train's engineer traveling on the train? (167Hz, 136Hz)



Given:

Frequency of the source = f = 150 Hz
Speed of the sound of the source = a = 35.0 m s⁻¹
Speed of the sound = v = 340 m s⁻¹

To Find:

(a) The apparent frequency when the train approaches towards the stationary person (observer)  = f' = ?  

The apparent frequency when the train moves away from the stationary person (observer)  = f'' = ? 

(b) Frequency observed by the train's engineer traveling on the train?



Solution:


(a) The formula for apparent frequency f' when the train approaches the stationary person (observer)  is


f' = `\frac {v}{v - a}` f


f' = `\frac {340 m s⁻¹}{340 m s⁻¹ - 35.0 m s⁻¹}` ｘ 150 Hz

by simplifying 

f' = 167.213 Hz

or

f' = 167 Hz ------------------Ans



And when after the train (source) passes then the apparent frequency f'' is given by 


f'' = `\frac {v}{v + a}` f


f'' = `\frac {340 m s⁻¹}{340 m s⁻¹ + 35 m s⁻¹}` ｘ 150 Hz

by simplifying 


f'' = 136 Hz ------------------Ans



(b) Frequency observed by the train's engineer traveling on the train:

Since the train (source) and the train's engineer traveling on the train are moving in the same direction with the same speed as the train so there will be no Doppler effect (i.e. No apparent frequency between the source and the observer)

Similar Questions:

A sound source vibrates at 200 Hz and is receding from a stationary observer at 18 ms⁻¹. If the speed of sound is 331 ms⁻¹ then what frequency does the observer hear? (189.68Hz) 


A train sounds its horn before it sets off from the station and an observer waiting on the platform estimates its frequency at 1200 Hz. The trains then moves off and accelerates steadily. Fifty seconds after departure, the driver sounds the horn again and the platform observer estimates the frequency of 1140 Hz. Calculate the train speed 50 s after departure. How far from the station is the train after 50 s? (Speed of sound = 340 m s⁻¹). (Ans: 17.9 m s⁻¹, 448 m)




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