A source of sound with frequency 1000 Hz moves at right angles to a wall with a velocity `u=17(cm)/(s)`. Two stationary receivers `R_1` and `R_2` are located on a straight line coinciding with the path of the source in the following succession: `R_1rarrsourceR_2wall`. Which receiver registers beating and what is the beat frequency? The velocity of sound is `c=340(m)/(s)`.

Explanation

`R_2` is approached by the source and the image source at the same speed so `R_2` receives waves of the same frequency and hence, it does not register beats. `R_1` is approached by the image source while the source itself recedes from it Hence it it receives waves of different wavelength so it registers beats.
`N_1`(apparent frequency of the source wave)
`=(340-0)/(340-(0.17))xx1000=1000.5Hz`
`N_2`(apparent frequency of the reflected wave)
`=(340-0)/(340+0.17)xx1000=999.5Hz`
Therefore beats registered`=1000.5-999.5=1.0Hz`