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

Q: 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

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.

Question

Agraph $A$ with slope $ = \,\frac{{{f_0}}}{{\left( {v + {v_s}} \right)}}$
Bgraph $B$ with slope $ = \,\frac{{{f_0}}}{{\left( {v - {v_s}} \right)}}$
Cgraph $A$ with slope $ = \,\frac{{{f_0}}}{{\left( {v - {v_s}} \right)}}$
Dgraph $B$ with slope $ = \,\frac{{{f_0}}}{{\left( {v + {v_s}} \right)}}$

JEE MAIN 2015, Diffcult

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