Question

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.

Answer 1

The number of revolutions per second is 2. Radius of the circle is `1.988m`.
The linear velocity of the tuning fork is
`v=2xx2pir=4xx(22)/(7)xx1.988=25(m)/(s)`
i. Apparent frequency when the tuning fork is approaching the listener is
`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 is
`n_2=(vn)/(v+v_s)=(350N)/((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`