Question

A train is approaching with velocity $25m{s}^{-1}$ towards a pedestrian standing on the track, frequency of horn of train is $1kHz$. The frequency heard by the pedestrian is (take, $v=350m{s}^{-1}$ )

• A. $1077Hz$
• B. $1167Hz$
• C. $985Hz$
• D. $954Hz$

Answer 1

The correct option is A

$1077Hz$

Step1: Given data and assumptions.

The velocity of sound, $v_s=25m{s}^{-1}$

The actual frequency of the horn, $f=1kHz=1000Hz$

The velocity of the sound wave, $v=350m{s}^{-1}$

Step2: Find the frequency heard by the pedestrian.

Formula used:

$f\text{'}=\left(\frac{v+v_0}{v-v_s}\right)\times f$

Where,

$f\text{'}$is the apparent frequency,

$f$ is the actual frequency,

$v$ is the sound wave velocity,

$v_0$ is observer velocity,

$v_s$ is the sound velocity.

Now,

$f\text{'}=\left(\frac{v+v_0}{v-v_s}\right)\times f$

$\Rightarrow$$f\text{'}=\left(\frac{350+0}{350-25}\right)\times 1000$ $\left[\because v_0=0\right]$

$\Rightarrow$$f\text{'}=1077Hz$

Hence, option A is correct. The frequency heard by the pedestrian is $1077Hz$.