Question 28: Waves

Question

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 observers were to move towards the source with speed $$v_0$$, one of the following two graphs (A and B) will give 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

Accepted Answer

According to Doppler's effect, the apparent frequency or sound when both source and observer are moving towards each other
$$ \Rightarrow f = {{(v + {v_0}){f_0}} \over {(v - {v_0})}}$$
$$ \Rightarrow f = \left( {{v \over {v - {v_s}}}} \right){f_0} + \left( {{{{v_0}} \over {v - {v_s}}}} \right){f_0}$$
$$ \Rightarrow f = \left( {{{{f_0}} \over {v - {v_s}}}} \right){v_0} + \left( {{{{f_0}} \over {v - {v_s}}}} \right)v$$
Equation of straight line, $$y=mx+c$$ which is equation of straight line making an intercept $$c$$ on Y-axis,
Slope of the graph $$ = {{{f_0}} \over {v - {v_s}}}$$ and intercept $$ = {{v{f_0}} \over {v - {v_s}}}$$
This condition is represented in graph A plotted between $$f$$ and $$v_0$$.
Hence, option (c) is correct.

Answer

graph A with slope $$ = {{{f_0}} \over {(v + {v_s})}}$$

Answer

graph B with slope $$ = {{{f_0}} \over {(v - {v_s})}}$$

Answer

graph A with slope $$ = {{{f_0}} \over {(v - {v_s})}}$$

Answer

graph B with slope $$ = {{{f_0}} \over {(v + {v_s})}}$$

Waves

Choose the correct answer: