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NEET
Exam
NEET
Subject
Physics
Chapter
Waves and Sound

NEET · Physics · Waves and Sound

A source of sound emits sound waves at frequency f_0 . It is moving...

A source of sound emits sound waves at frequency f0f_0. It is moving towards an observer with fixed speed vs(vs<vv_s\left(v_s < v\right., where vv is the speed of sound in air.) If the observers were to move towards the source with speed v0v_0, one of the following two graphs (A(A and B)B) will give the correct variation of the frequency ff heard by the observer as v0v_0 is changed.A source of sound emits sound waves at frequency f_0 . It is moving towards an observer with fixed speed v_s(v_s The
A source of sound emits sound waves at frequency f_0 . It is moving towards an observer with fixed speed v_s(v_s The
The variation of ff with v0v_0 is given correctly by

Options

  1. A\operatorname{graph} Awithslopewith slope=\frac{f_0}{\left(v+v_s\right)}
  2. Bgraph BB with slope $=\frac{f_0}{\left(v-v_s\right)}
  3. Cgraph AA with slope $=\frac{f_0}{\left(v-v_s\right)}
  4. Dgraph BB with slope $=\frac{f_0}{\left(v+v_s\right)}

Correct answer

C. graph AA with slope $=\frac{f_0}{\left(v-v_s\right)}

Step-by-step solution

According to Doppler's effect, the apparent frequency of sound when both source and observer are moving towards each other ⇒f=(v+v0)f0(v−v0)⇒f=(vv−vs)f0+(v0v−vs)f0\begin{array}{ll} \Rightarrow& f=\frac{\left(v+v_0\right) f_0}{ \left(v-v_0\right)}\\ \Rightarrow & f=\left(\frac{v}{v-v_s}\right)f_0+\left(\frac{v_0}{v-v_s}\right)f_0 \end{array} \Rightarrow \quad f=\left(\frac{f_0}{v-v_s}\right)v_0+\left(\frac{f_0}{v-v_s}\right)v Equation of straight line, y=mx+cy=m x+c which is equation of straight line making an intercept cc on YY-axis, Slope of the graph =\frac{f_0}{v-v_s} and intercept =\frac{v f_0{ }^{{}^{\circ}}}{v-v_s} This condition is represented in graph A plotted between ff and v0v_0. Hence, option (c) is correct.
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