A source of sound emits sound waves at frequency f_0. It is movin… - Vidyadip

MCQ

A source of sound emits sound waves at frequency $f_0$. It is moving towards an observer with fixed speed $v_s$ ($v_s < v$, where $v$ is the speed of sound in air). If the observer were to move towards the source with speed $v_0$, one of the following two graphs ($A$ and $B$) will given the correct variation of the frequency $f$ heard by the observer as $v_0$ is changed The variation of $f$ with $v_0$ is given correctly by

A
graph $A$ with slope $ = \,\frac{{{f_0}}}{{\left( {v + {v_s}} \right)}}$
B
graph $B$ with slope $ = \,\frac{{{f_0}}}{{\left( {v - {v_s}} \right)}}$
✓
graph $A$ with slope $ = \,\frac{{{f_0}}}{{\left( {v - {v_s}} \right)}}$
D
graph $B$ with slope $ = \,\frac{{{f_0}}}{{\left( {v + {v_s}} \right)}}$

✓

Answer

Correct option: C.

graph $A$ with slope $ = \,\frac{{{f_0}}}{{\left( {v - {v_s}} \right)}}$

c
According to Doppler's effect,

Apparent, frequency $f=\left(\frac{V+V_{0}}{V-V_{S}}\right) f_{0}$

Now, $f=\left(\frac{f_{0}}{V-V_{S}}\right) V_{0}+\frac{V f_{0}}{V-V_{s}}$

So, slope $=\frac{f_{0}}{V-V_{S}}$

Hence, option $(c)$ is the correct answer.

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