The apparent frequency of a sound wave as heard by an observer is… - Vidyadip

MCQ

The apparent frequency of a sound wave as heard by an observer is $10\%$ more than the actual frequency. If the velocity of sound in air is $330\,m/sec$ , then

$(i)$ The source may be moving towards the observer with a velocity of $30\,ms^{-1}$

$(ii)$ The source may be moving towards the observer with a velocity of $33\,ms^{-1}$

$(iii)$ The observer may be moving towards the source with a velocity of $30\,ms^{-1}$

$(iv)$ The observer may be moving towards the source with a velocity of $33\,ms^{-1}$

A
$ii,\, iv$
B
$ii,\,iii$
✓
$i,\,iv$
D
$iii,\,iv$

✓

Answer

Correct option: C.

$i,\,iv$

c
$f_{\mathrm{app}}=f_{\mathrm{actual}}+10 \%$ of factual

$=\mathrm{f}+\frac{10}{100} \mathrm{f}=1.1 \mathrm{f}=\mathrm{f}\left[\frac{\mathrm{v}-\mathrm{v}_{0}}{\mathrm{v}-\mathrm{v}_{\mathrm{s}}}\right]$

$\Rightarrow \frac{v-v_{0}}{v-v_{s}}=1.1$

if $v_{0}=0 \Rightarrow v=1.1 \mathrm{v}-1.1 \mathrm{v}_{\mathrm{s}}$

$\Rightarrow v_{s}=\frac{0.1 \mathrm{v}}{1.1}=\frac{330}{11}=30 \mathrm{\,m} / \mathrm{sec}$

$\mathrm{v}_{\mathrm{s}}=30 \mathrm{\,m} / \mathrm{s}$

[source moving towards stationary observer]

Case $II \,:$ $v_{s}=0$

$\Rightarrow 1.1=\left[\frac{\mathrm{v}-\mathrm{v}_{0}}{\mathrm{v}}\right]$

$\Rightarrow 1.1 \mathrm{v}=\mathrm{v}-\mathrm{v}_{0}$

$\Rightarrow \mathrm{v}_{0}=-0.1 \mathrm{v}$

$\mathrm{v}_{0}=-33 \mathrm{\,m} / \mathrm{sec}$

(observer moving towards source)

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