Question

Two sirens situated one kilometre apart are producing sound of frequency $330Hz$. An observer starts moving from one siren to the other with a speed of $2m/s$. If the speed of sound be $330m/s$, what will be the beat frequency heard by the observer?

• A. $6$
• B. $1$
• C. $8$
• D. $4$

Answer 1

The correct option is D $4$


We know that:
$n_1=n\left(\frac{v-v_0}{v}\right)$

$n_2=n\left(\frac{v+v_0}{v}\right)$

Given, actual frequency of the sirens, $n=330Hz$
velocity of the observer $v_0=2m/s$
velocity of sound $v=330m/s$
Beat frequency $=$ ?

Let consider observer is moving away from siren $1$ and towards siren $2$.

Hearing frequency of sound emitted by siren $1$,
$n_1=n\left(\frac{v-v_0}{v}\right)$

$n_1=330Hz\times \left(\frac{330-2}{330}\right)$

$n_1=328Hz\dots \left(i\right)$

Now, Hearing frequency of sound emitted by siren $2$,
$n_2=n\left(\frac{v+v_0}{v}\right)$

$n_2=330Hz\times \left(\frac{330+2}{330}\right)$

$n_2=332Hz\dots \left(ii\right)$

Now,
Beat frequency $=n_2-n_1$
Beat frequency $=332-328$
Beat frequency $=4Hz$

Final answer: (b)