Question

A speeding motorcyclist sees traffic jam ahead him. He slows down to $36 \,km$ hour $^{-1}$. He finds that traffic has eased and a car moving ahead of him at $18 \,km$ hour $^{-1}$ is honking at a frequency of $1392 \,Hz$. If the speed of sound is $343\,ms^{-1}$ 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, $v_{m}=36 \,km\, hour ^{-1}$
$=36 \times \frac{5}{18}=10 \,ms ^{-1}$
Speed of car,
$v_{c}=18\, km \,hour ^{-1}=18 \times \frac{5}{18} \,ms ^{-1}=5 \,ms ^{-1}$
Frequency of source, $v_{0}=1392 \,Hz$
Speed of sound, $v=343\, ms ^{-1}$
The frequency of the honk heard by the motorcyclist is
$v^{\prime}=v_{0}\left(\frac{v+v_{m}}{v+v_{c}}\right)=1392\left(\frac{343+10}{343+5}\right)$
$=\frac{1392 \times 353}{348}=1412\, Hz$