Question

A man standing on a platform observe that the frequency of the sound of a whistle emitted by a train drops by $140Hz$. If the velocity of sound in air is $330m/s$ and the speed of the train is $70m/s$, the frequency of the whistle is

• A. $571Hz$
• B. $800Hz$
• C. $400Hz$
• D. $260Hz$

Answer 1

The correct option is B $800Hz$

The question is based on Doppler effect. We can write a formula for apparent frequency $\left(f^{\prime }\right)$ where a source ( train ) is moving away from the observation ( man ).

$\Rightarrow f^{\prime }=\frac{vf}{vfu}$

$\Rightarrow f^{\prime }=$ Apparent frequency

$v=$ velocity of sound in air $=330m/s$

$f=$ real frequency

$u=$ velocity of source $=70m/s$

Now we can substitute above values into the formula

$\Rightarrow f^{\prime }=\frac{330f}{330+70}$

$=\frac{330f}{400}$

$=\frac{33f}{40}⟶\left(1\right)$

But we know that,

real frequency $-$ apparent frequency $=140Hz$

$\Rightarrow f-f^{\prime }=140$

$\Rightarrow f-\frac{33f}{40}=140$

$\Rightarrow \frac{7f}{40}=140$

$\Rightarrow f=140\times \frac{40}{7}$

$\therefore$ Frequency of the whistle $=800Hz.$

Hence, the answer is $800Hz.$