Question

Two tuning forks A and B having a frequency of 500 Hz each are placed with B to the right of A. An observer in between the forks in moving towards B with a speed of 25 m/s. The speed of sound is 345 m/s and the wind speed is 5 m/s from A to B. Calculate the difference in the two frequencies heard by observer.

Answer 1

Let the fork at A be source `S_1` and the fork at B source `S_2`. For the sound from `S_1`:
Apparent frequency`=f_1=f((c-V_0)/(c-V_S))`
Here `c=345+5=350(m)/(s)` as wind and sound are in same direction
`V_0=+25(m)/(s)` ,`V_S0(m)/(s)`
`impliesf_1=500((350-25)/(350-0))=464.3Hz`
for sound from source `S_2`:`c=345-5=340(m)/(s)` as wind is in oppsite direction to that of sound.
`V_S=0(m)/(s)`,`V_0=-25(m)/(s)`
`impliesf_2=f((c-V_0)/(c-V_S))=500((c-(-25))/(c-0))=(500xx365)/(340)`
`=536.80Hz`
`impliesf_2-f_1=(536.80-464.30)=72.5Hz`