Question

A speeding motorcyclist sees traffic jam ahead him. He slows down to $36km$ hour ${}^{-1}$. He finds that traffic has eased and a car moving ahead of him at $18km$ hour ${}^{-1}$ is honking at a frequency of $1392Hz$. If the speed of sound is $343m{s}^{-1}$ the frequency of the honk as heard by him will be

• A. 1332 Hz
• B. 1372 Hz
• C. 1412 Hz
• D. 1454 Hz

Answer 1

Answer: (C)

Here, speed of motorcyclist, $v_m=36kmhou{r}^{-1}$
$=36\times \frac{5}{18}=10m{s}^{-1}$
Speed of car,
$v_c=18kmhou{r}^{-1}=18\times \frac{5}{18}m{s}^{-1}=5m{s}^{-1}$
Frequency of source, $v_0=1392Hz$
Speed of sound, $v=343m{s}^{-1}$
The frequency of the honk heard by the motorcyclist is
$v^{\prime }=v_0\left(\frac{v+v_m}{v+v_c}\right)=1392\left(\frac{343+10}{343+5}\right)$
$=\frac{1392\times 353}{348}=1412Hz$