A train approaching a hill at a speed of 40 km/h sounds a whistle of frequency 580 Hz when it is at a…
A train approaching a hill at a speed of 40 km/h sounds a whistle of frequency 580 Hz when it is at a distance of 1 km from a hill. A wind with a speed of 40 km/h is blowing in the direction of motion of the train. Find the frequency of the whistle as heard by an observer on the hill.
(Take, speed of sound in air = 1200 km/h)
400 Hz
500 Hz
600 Hz
350 Hz
Solution
Speed of sound in air, $v = 1200 \text{ km/h}$
Speed of source, $v_s = 40 \text{ km/h}$
Speed of wind, $w = 40 \text{ km/h}$
Frequency emitted by source, $f = 580 \text{ Hz}$
[Diagram showing source $S$ moving with speed $v_s$ towards a hill at point $O$ at distance $1 \text{ km}$, with sound velocity $v$ and wind velocity $w$ directed towards the hill.]
Frequency received at hill,
$f' = f \left(\frac{v + w - v_o}{v + w - v_s}\right) = 580 \left(\frac{1200 + 40 - 0}{1200 + 40 - 40}\right)$
$= 599.33 \text{ Hz} \approx 600 \text{ Hz}$