A vibrating tuning fork tied to the end of a string 1.988 m long is whirled round a circle. If it makes two revolutions in a second, calculate the ratio of the frequencies of the highest and the lowest notes heard by an observer situated in the plane of the tuning fork. Valocity of sound is 350 m/s.

Explanation

Number of revolutions per second = 2
Radius of the circle = 1.988 m
As Linear velocityof the tuning fork is
`v = 2xx2 pir = 4 xx (22)/(7) xx 1.988` = 25m//s
(i) Apparent frequency when the tuning fork is approaching the listener
`n_(1) = (vn)/(v - v_(s) ) = (350n)/(350 - 25) = (14)/(13) n`
(ii) Apparent frequency when the tuning fork is moving away from the listener
`n_(2) = (vn)/(v + v_(s)) = (50n)/((350+25)) = (14)/(15)n`
The ratio of highest note to the lowest note is given by
`(n_(1))/(n_(2)) = (14n)/(13) xx (15)/(14n) = (15)/(13)` = 1.154