A military band was marching on a street in the same direction as the normal traffic flow. A motorist was approching the band from behind in his car just at the moment when they were playing the musical note `A` (frequency `440 Hz`) in unison. The same band' performance was also simultaneously being broad live on the ratio from a stationary microphone which was situated on the sidewalk just ahead of the band. The motorist noticed that the combination of the direct sound coming from the band ahead of the band brodcast produced discernible beats. Timing the beats, he counted `4` beats in `3`seconds. He noted from the speedmeter that his car was travelling at `18` kilometers per hour.
Calculate the speed in meters per seconds at which the band was marching assuming that the speed of sound on that day was `330 ms^(-1)`. (It was a very cold day)

Answer

`v = 1.958 ms^(-1)` or `2.98 m//s`

Explanation

Let speed of band be `v ms^(-1)`
Speed of car is `(18000)/(3600) = 5 ms^(-1)`
Apparent frequency at microphone `= (330 - 0)/(330 - v) xx f_(0)`
Apparent frequency at car `= (330 + 5)/(330 + v)f_(0)`
`= (335)/(330 + v)f_(0)`
Difference in frequency `= (4)/(3)`
`:. (335)/(330 + v) - (330)/(330 - v) = (+-4)/(3 xx 440) = 1.985 ms^(-1)` or `2.98 m//s`