A speeding motorcyclist sees traffic jam ahead of him. He slows down to $36\text{ km h}^{-1}$. He finds that…
A speeding motorcyclist sees traffic jam ahead of him. He slows down to $36\text{ km h}^{-1}$. He finds that traffic has eased and a car moving ahead of him at $18\text{ km h}^{-1}$ is honking at a frequency of 1392 Hz. If the speed of sound is $343\text{ ms}^{-1}$, then the frequency of the honk as heard by him will be
1332 Hz
1372 Hz
1412 Hz
1454 Hz
Solution
As, both observer and source are moving, we can use the formula of apparent frequency as
A diagram shows an observer moving at $36\text{ kmh}^{-1}$ towards a car moving at $18\text{ kmh}^{-1}$ emitting sound of frequency $f = 1392\text{ Hz}$.
$f = f_o \left(\frac{v + v_o}{v + v_s}\right) = 1392 \left(\frac{343 + 10}{343 + 5}\right)$
$= 1392 \left(\frac{353}{348}\right) = 1412\text{ Hz}$