Question

A source of sound (of frequency $f_0$ ) and an observer are moving towards the intersection point $P$ following two straight lines inclined at ${60}^{\circ }$ with speeds $v/2$ and $v/3$ respectively where $v$ is the speed of sound in air. If frequency of the sound heard by the observer when he reaches point $P$ (Assume that the observer reaches $P$ before source) is $n{f}_0,$ then the value of $3n$ is
[Answer upto two decimal points]

Answer 1

From given,
For apparant frequency, $f^{\prime }=\frac{f_0(v-v_0)}{(v-v_s)}$
$f^{\prime }=\frac{f_0(v-\frac{v}{3}cos{60}^{\circ })}{v-\frac{v}{2}}=f_0\left(\frac{v-\frac{v}{6}}{\frac{v}{2}}\right)=\frac{5f_0}{3}=$
$\therefore$ As the value of $n$ is $\frac{5}{3}$, so value of $3n$ is 5.