Question

A stationary source produces a note of frequency 350 Hz. An observer in a car moving towards the sources measures frequency of 370 Hz. Find Speed of a car.

Answer 1

Hint: In this question we will use the relation between the frequency and the velocity; next we will substitute the given values in the equation. This will give us the required result. We will also discuss the basics of speed and frequency for our better understanding.
Formula used:
$na = n(v + {v_0}/v)$
$na = n(v - {v_0}/v)$

Complete answer:
We have equation for frequency, when the observer in the car moves towards the stationary source, given by:
$na = n(v + {v_0}/v)$
Substituting the given values in above equation, we get:
$\eqalign{& 370 = 350(340 + {v_0}/340) \cr
  & \Rightarrow 359.42 = 340 + {v_0} \cr
  & \Rightarrow {v_0} = 19.43m/s \cr} $
Now, when the car moves towards the stationary source then our equation becomes:
$na = n(v - {v_0}/v)$
Here, substituting the given values in above equation, we get:
$\eqalign{& na = 350(340 - 20/340) \cr
  & \Rightarrow na = 35/34 \times 320 \cr
  & \therefore na = 329.41Hz \cr} $
Therefore, we get the required answers, i.e., the speed of the car is 19.43m/s and frequency of the sound measured by the observer in the car is given by 329.41 Hz.

Additional information:
We know the basic difference of speed and velocity i.e., speed is the measure of how fast an object can travel, whereas velocity tells us the direction of this speed. Speed is a scalar quantity that means it has only magnitude, whereas velocity is a vector quantity that means it has both magnitude and direction. The S.I unit of velocity is meter per second (m/sec).
Further, the frequency is defined as the number of waves that pass a fixed point in unit time. It can also be defined as the number of cycles or vibrations undergone during one unit of time. The S.I unit of frequency is Hertz or Hz and the unit of wavelength is meter or m. Furthermore we also know the S.I unit of time which is given by second or s.

Note:
Here, we should notice that the speed of sound is different in different mediums. Further, the speed that is more than the speed of sound is termed differently like- supersonic, hypersonic etc. we should also remember that the speed of light cannot be achieved by any other transport or object.