Question

QA speeding motorcyclist sees traffic jam ahead of him. He slows down to 36km/ hour. He finds that traffic has eased and a car moving ahead of him at 18km/ hour is honking at a frequency of 1392 Hz. If the speed of the sound is 343m/ s, 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

Hint: Here, both the motorcyclist and the car are moving, this means the honk heard by him will have an apparent frequency. Apparent frequency is the frequency perceived by an observer. It may or may not be equal to the value of actual frequency. So use the formula of apparent frequency to solve the question.

Formula used:
Apparent frequency of a sound is $f = {f_o}\left( {\dfrac{{v + {v_o}}}{{v + {v_s}}}} \right)$, where v is the velocity of sound, ${v_o}$ is the velocity of the observer, ${v_s}$ is the velocity of the source and ${f_o}$ is the actual frequency.

Complete step by step answer:
We are given that a speeding motorcyclist sees a traffic jam ahead of him and then he slows down to 36km/ hour and then he finds a car moving ahead of him at 18km/ hour is honking at a frequency of 1392 Hz.
We have to find the frequency of the honk sound as heard by him when the speed of sound is 343m/ s.
Here, the motorcyclist is travelling on a motorcycle and another person is travelling in a car.
And both the motorcycle and the car are moving. So the frequency of the sound produced by the car honk will be the apparent frequency.
Apparent frequency can be calculated using $f = {f_o}\left( {\dfrac{{v + {v_o}}}{{v + {v_s}}}} \right)$
Speed of the motorcycle and the car are given in km/ hour. So, convert them into m/ s by multiplying with $\dfrac{5}{{18}}$
$
  f = {f_o}\left( {\dfrac{{v + {v_o}}}{{v + {v_s}}}} \right) \\
  {f_o} = 1392Hz,v = 343m/s \\
  {v_o} = 36km/hour = 36 \times \dfrac{5}{{18}}m/s = 10m/s \\
  {v_s} = 18km/hour = 18 \times \dfrac{5}{{18}}m/s = 5m/s \\
   \implies f = 1392\left( {\dfrac{{343 + 10}}{{343 + 5}}} \right) \\
   \implies f = 1392 \times \dfrac{{353}}{{348}} \\
  \therefore f = 1412Hz \\
$
Therefore, the frequency of the honk as heard by the motorcyclist is 1412 Hz.

So, the correct answer is “Option C”.

Note:
 If the units of the same measurement are given irrelevantly, then convert all the irrelevant units into the same type of units. Here the speed of sound is given in m/ s and speeds of car and motorcyclist are given in km/ hour. So we multiplied the speeds of cars and motorcyclists by $\dfrac{5}{{18}}$ to convert them into m/s. If the units are given in m/s and we have to convert them into km/hour, then multiply the units with $\dfrac{{18}}{5}$.