Question

A train, at rest blows a whistle of frequency 600Hz in still air. What is the frequency of whistle for a platform observer when the train (a) approaches the platform with the speed of 15ms-1. (b) recedes from the platform with the speed of 15ms-1. What is the speed of sound in each case? Speed of sound in air is 345ms-1.

Answer 1

Answer:

Explanation:

(a)Frequency of the whistle, v=400Hzv=400Hz

Speed of the train, v_T=10\,m/sv

T

​

=10m/s

Speed of sound, v=340\,m/sv=340m/s

The apparent frequency (v')(v

′

) of the whistle as the train approaches the platform is given by the

relation:

\displaystyle v'=\left(\frac{v}{v-v_r}\right)vv

′

=(

v−v

r

​

v

​

)v

   =\displaystyle \left(\frac{340}{340-10}\right)\times 400=412.12Hz=(

340−10

340

​

)×400=412.12Hz

(b) The apparent frequency (v')(v

′

) of the whistle as the train recedes from the platform is given by the relation:

\displaystyle v''=\left(\frac{v}{v+v_r}\right)vv

′′

=(

v+v

r

​

v

​

)v

   \displaystyle =\left(\frac{340}{340+10}\right)\times 400=388.57\,Hz=(

340+10

340

​

)×400=388.57Hz

(ii) The apparent change in the frequency of sound is caused by the relative motions of the source and the observer. These relative motions produce no effect on the speed of sound. Therefore, the speed of sound in air in both the cases remains the same, i.e., 340 m/s.

Answer 2

(a). The frequency of whistle is 627.27 Hz.

(b). The frequency of whistle is 575 Hz.

(c). The speed of sound in each case is same.

Explanation:

Given that,

Frequency = 600 Hz

Speed of train = 15 m/s

Speed of sound = 345 m/s

(a).  We need to calculate the frequency of whistle

The apparent frequency of the whistle as the train approaches the platform is given by

Using formula of speed

$f'=(\dfrac{v}{v-v_{r}})f$

Put the value into the formula

$f'=(\dfrac{345}{345-15})\times600$

$f'=627.27\ Hz$

The frequency of whistle is 627.27 Hz.

(b). We need to calculate the frequency of whistle

The apparent frequency of the whistle as the train recedes from the platform is given by

Using formula of speed

$f'=(\dfrac{v}{v+v_{r}})f$

Put the value into the formula

$f'=(\dfrac{345}{345+15})\times600$

$f'=575\ Hz$

The frequency of whistle is 575 Hz.

(c). The speed of sound in each case is same.

Hence, (a). The frequency of whistle is 627.27 Hz.

(b). The frequency of whistle is 575 Hz.

(c). The speed of sound in each case is same.

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Topic : frequency

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