Question

The driver of a car traveling with a speed of 30 m/s towards a hill sounds a horn of frequency 600 Hz. If the velocity of sound in air is 330 m/s, the frequency of reflected sound as heard by the driver is then:
A). 555.5Hz
B). 720Hz
C). 500Hz
D). 550Hz

Answer 1

Hint: In this question, we will use the relation between frequency and speed; this will give us the required result of the frequency of reflected sound as heard by the driver. Further, we will discuss the basic concept of sound and frequency, for our better understanding.
Formula used:
$n' = \dfrac{v}{{v - {v_s}}} \times n$
$n'' = \dfrac{{v + {v_1}}}{v} \times n'$

Complete step-by-step solution
Here, as we know that the source is moving towards the hill, so apparent frequency of horn striking the wall is given by:
$n' = \dfrac{v}{{v - {v_s}}} \times n$
Substituting the given values in the above equation, we get:
$\eqalign{
  & n' = \dfrac{{330}}{{330 - 30}} \times 600 \cr
  & \Rightarrow n' = 330 \times 2 \cr
  & \Rightarrow n' = 660Hz \cr} $
Now, as we know that for the reflected sound, driver acts as listener moving towards source, frequency is given as:
$n'' = \dfrac{{v + {v_1}}}{v} \times n'$
$n'' = \dfrac{{v + {v_1}}}{v} \times n'$
Substituting the given values in the above equation, we get:
$\eqalign{& n’’ = \dfrac{{330 + 30}}{{330}} \times 600 \cr
  & \Rightarrow n’’ = 360 \times 2 \cr
  & \therefore n’’ = 720Hz \cr} $
Therefore, we get the required result which gives the frequency of reflected sound as heard by the driver is given by the above result.
Additional information: We know the basic difference between 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. further, 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.