A speaker emits a sound wave of frequency f_0. When it moves towa… - Vidyadip

MCQ

A speaker emits a sound wave of frequency $f_0$. When it moves towards a stationary observer with speed $u$, the observer measures a frequency $f_1$. If the speaker is stationary and the observer moves towards it with speed $u$, the measured frequency is $f_2$. Then,

A
$f_1=f_2 < f_0$
✓
$f_1 > f_2$
C
$f_1 < f_2$
D
$f_1=f_2 > f_0$

✓

Answer

Correct option: B.

$f_1 > f_2$

b
(b)

When observer is stationary and source is moving, observed frequency is

$f_1=f_0\left(\frac{v}{v-u}\right)$

where, $v=$ speed of sound and $u=$ speed of source.

When source is stationary and the observer is moving towards source, then measured frequency is

$f_2=f_0\left(\frac{v+u}{v}\right)$

So, difference in frequencies observed is

$f_2-f_1=f_0\left(\frac{v+u}{v}-\frac{v}{v-u}\right)$

$=-\frac{u^2 f_0}{v(v-u)}$

$\Rightarrow \quad f_2-f_1 < 0 \text { or } f_2 < f_1$

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