A police car moving with speed 5 m/s is blowing a siren of frequency 600 Hz and travelling towards a vertical wall. Calculate
(a) number of beats heard in 1 s by driver of car.
(b) beats heard by a person standing between car and well.
(c) beats heard by a person standing behind the car. (Speed of sound is 340 m/s)

Explanation

v = speed of sound = 340 m/s
v = 600 Hz, `u_(s)` = speed of car = 5 m/s
(a) Two sounds will be heard by the driver, one coming directly from the siren and the other sound which is reflected by the wall.
As driver is moving towards the wall and in the right direction and the reflected image is approaching towards the driver with same speed towards left.
Therefore, frequency of sound heard by driver
`v. = v(upsilon + upsilon_(L))/(upsilon - u_(s)) " "upsilon_(L) = upsilon_(S) = 5` m/s
`= 600 xx((340 +5)/(340 - 5))`
= 618 Hz
No. of beats heard/sec. = v. - v
= 618 - 600
= 18
Beat frequency = 610 - 600 = 18 Hz
(b) A person standing at the mid-point of car and wall will hear two sounds. One sound is from the siren approaching him and the other is the reflected sound of the siren approaching towards him with same speed. Hence, he will hear no beats.
(c) A person standing behind the car, at point N, will again hear two sounds. One is from the siren receding away from him and other is from the reflected sound of the siren approaching towards him with the same speed.
`v_(1) = ((upsilon)/(upsilon + u_(s)))v = ((340)/(340 + 5)) xx 600`
= 591.3 Hz
`v_(2) = ((upsilon)/(upsilon - u_(s)))v = ((340)/(340 - 5)) 600`
= 609 Hz
Beat frequency `= v_(2) - v_(1) = 609 - 6=591` = 18 Hz