A person with vibrating tuning fork of frequency 338Hz is moving towards a vertical wall with a speed of `2 ms^(-1)`. Velocity of sound in air is `340 ms^(-1)`. The number of beats heard by that person per second is

Options

A. 2
B. 4
C. 6
D. 8

Answer

B

Explanation

Frequency of tuning fork (source), v= 338Hz Velocity of sound, `v= 340 ms^(-1)`
When the person is moving towards the wall, the frequency of sound reaching the wall is
`v' = (v v)/(v-v_(S))` …(i)
On reflection wall acts as source and person is the listener moving towards the source. So the frequency heard by the person after reflection from the wall is
`v'' = [(v+v_(1))/(v-v_(S))] v'` ...(ii)
Substituting the value of v' from Eq. (i) in (ii), we get
`v'' = [(v+v_(1))/(v-v_(S))] v= ((v + v_(S))/(v- v_(S))) v " " ["As " v_(L) = v_(S)]`
`=[(340 + 2)/(340-2)] 338 = (342)/(338) xx 338 = 342 Hz`
`:.` Number of beats heard per second `= v'' -v`
`= 342-338 = 4`