Question

A stationary car sounds a siren with a frequency of $900Hz$. If the speed of sound is $300\ m/s$, an observer driving towards the car with a speed of $33\ m/s$, will hear a frequency of
(a) $891Hz$
(b) $900Hz$
(c) $1089Hz$
(d) $1100Hz$

Answer 1

Hint: The driver driving the car hears the sound of horn from a stationary car due to doppler’s effect which can be given as, change in frequency of a wave in relation to an observer who is moving either tards the object or going away from the object. Using this principle, we will find the frequency of the horn coming from a stationary car.
Formula used:
${{f}_{p}}=f\left( \dfrac{v+{{v}_{o}}}{v} \right)$

Complete answer:
In question we are given that, A stationary car sounds a siren with a frequency of $900Hz$. Now, if the speed of sound is $300\ m/s$, an observer driving towards the car with a speed of $33\ m/s$, then what will be the frequency of sound of the siren. This effect takes place due to Doppler’s effect. So, before finding the answer we will understand what doppler effect is.

Doppler effect can be stated as ” The Doppler effect (or the Doppler shift) is the change in frequency of a wave in relation to an observer who is moving relative to the wave source.” It can be seen mathematically as,

${{f}_{p}}=f\left( \dfrac{v+{{v}_{o}}}{v} \right)$

Where, ${{f}_{p}}$ is the frequency heard by the observer, $f$ is the frequency of source, $v$ is velocity sound of source and ${{v}_{o}}$ is the velocity of observer.
Now, in question we are given that the frequency of source of siren is $900Hz$, velocity of sound of source is $300\ m/s$ and velocity of observer going towards the object is $33\ m/s$, on substituting these values we will get,

${{f}_{p}}=900\left( \dfrac{330+33}{330} \right)$
$\Rightarrow {{f}_{p}}=900\left( \dfrac{363}{330} \right)=1089Hz$
Thus, the frequency of sound heard by the observer is $1089Hz$.

So, the correct answer is “Option C”.

Note:
In this question it is given that the observer is going towards the siren or source so here we have added the velocities of source and observer i.e. $v+{{v}_{o}}$, if the observer is moving away from the source then we have subtract two velocities such as, $v-{{v}_{o}}$. So, students must take care about this while solving the problem.