Question

A train is moving on a straight track with speed $ 20m/s $ . It is blowing its whistle at the frequency of $ 1000Hz $ . The percentage change in the frequency heard by a person standing near the track as the train passes him is (speed of sound $ = 320m/s $ ) close to :
(A) $ 6\% $
(B) $ 12\% $
(C) $ 18\% $
(D) $ 24\% $

Answer 1

Hint : To solve this question we have to know about frequency and how to calculate the percentage change. We know that, Frequency is the number of occurrences of a repeating event per unit of time. It is also referred to as temporal frequency, which emphasizes the contrast to spatial frequency and angular frequency. Frequency is measured in hertz (Hz) which is equal to one occurrence of a repeating event per second. We also can say that, Frequency is the number of occurrences of a repeating event per unit of time. It is also referred to as temporal frequency, which emphasizes the contrast to spatial frequency and angular frequency.

Complete Step By Step Answer:
Let us consider,
 The train approaches frequency is $ {f_1} = 1000(\dfrac{{320}}{{320 - 20}}) = 1000(\dfrac{{320}}{{300}})Hz $
Again, train reduces with the frequency of $ {f_2} = 1000(\dfrac{{320}}{{320 + 20}}) = 1000(\dfrac{{320}}{{340}})Hz $
Now, we have to calculate the percentage change,
 $ \Delta f = (\dfrac{{{f_1} - {f_2}}}{{{f_1}}}) \times 100\% $
 $ = \left( {1 - \dfrac{{300}}{{340}}} \right) \times 100\% $
 $ = \dfrac{{40}}{{340}} \times 100\% $
 $ = 11.7\% $
 $ \approx 12\% $
So, the right option will be option number B.

Note :
We have to know to calculate the percentage change. In mathematics, the concept of percent change is used to describe the relationship between an old value and new value. Specifically, the percent change expresses the difference between the old and new values as a percentage of the old value. We have used this as a formula to calculate the percentage change.