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A student holds a tuning fork oscillating at $170 \mathrm{~Hz}$. He walks towards a wall at a constant speed of $2 \mathrm{~ms}^{-1}$. The beat frequency observed by the student between the tuning fork and its echo is (Velocity of sound $=340 \mathrm{~ms}^{-1}$ )
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The correct answer is:
$2 \mathrm{~Hz}$
From Doppler's effect, apparent frequency,
$n^{\prime}=\left(\frac{v+v_0}{v-v_0}\right) n$
or, $n^{\prime}=\left(\frac{340+2}{340-2}\right) \times 170$
or, $\quad n^{\prime}=\frac{342}{338} \times 170$
or $\quad n^{\prime}=172.01=172 \mathrm{~Hz}$
Therefore, beat frequency observed
$(172-170)=2 \mathrm{~Hz}$
$n^{\prime}=\left(\frac{v+v_0}{v-v_0}\right) n$
or, $n^{\prime}=\left(\frac{340+2}{340-2}\right) \times 170$
or, $\quad n^{\prime}=\frac{342}{338} \times 170$
or $\quad n^{\prime}=172.01=172 \mathrm{~Hz}$
Therefore, beat frequency observed
$(172-170)=2 \mathrm{~Hz}$
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