Question

Two factories are sounding sirens at $800\text{Hz}$. A man goes from one factory to the other at a speed of $2\text{m/s}$. The velocity of sound is $320\text{m/s}$. The number of beats heard by the person in $1\text{s}$ will be

• A. $10\text{Hz}$
• B. $20\text{Hz}$
• C. $8\text{Hz}$
• D. $5\text{Hz}$

Answer 1

The correct option is A $10\text{Hz}$

Let the frequency of sound by the man heard be $n^{\prime }$ , When he is approaching the factory.$$n^{\prime }=\left(\frac{v+v_0}{v}\right)n$$ $n^{\prime }=\left(\frac{320+2}{320}\right)=\frac{322}{320}\times 800$

Let the frequency of sound by the man heard be $n^{\prime \prime }$ , when he is receding from the factory.$$n^{\prime \prime }=\left(\frac{v-v_0}{v}\right)n$$ $n^{\prime \prime }=\left(\frac{320-2}{320}\right)\times 800=\frac{318}{320}\times 800$

Thus,

Beat frequency $n=n^{\prime \prime }-n^{\prime }$

$\Rightarrow n=\left(\frac{322-318}{320}\right)\times 800=10\text{Hz}$

Hence, option (a) is the correct answer.