Question

A source of sound emitting a 1200 Hz note travels along a straight line at a speed of $170m{s}^{-1}$. A detector is placed at a distance of 200 m from the line of motion of the source. (a) Find the frequency of sound received by the detector at the instant when the source gets closest to it. (b) Find the distance between the source and the detector at the instant it detects the frequency 1200 Hz. Velocity of sound in air $=340m{s}^{-1}$.

Answer 1

Here, $V_S=170$ m/s

$n_0=1200Hz$

(a)The frequency of sound received by deterctor (when source gets closest to it)

$=\frac{v}{v-v_{s}cosv}\times n_0$

$=\frac{340}{340-170\times \frac{115.47}{230.94}}\times 1200$

=1600 Hz

(b)The detector will detect 1200 Hz frequency for energy emitted at minimum distance.

Then, $\frac{200}{340}=\frac{x}{170}$

$\Rightarrow x=100m$

SO, Required distance

$=\sqrt{(200{)}^2+x^2}=\sqrt{(200{)}^2+(100{)}^2}$

=224 m