A stationary observer receives sonic oscillations from two tuning forks one of which approaches and the other recedes with the same velocity. As this takes place, the observer hears the beats of frequency `f = 2.0 H_(Z)`. Find the velocity of each tuning fork if their oscillation frequency is `f_(o) = 680 H_(Z)` and the velocity of sound in air is `upsilon = 340 m//s`.

Options

A. 1m/s
B. 2m/s
C. 0.5m/s
D. 1.5m/s

Answer

C

Explanation

let both tuning forks move with speed `v_(S)`. Then the beat frequency heard by stationary observer is
`680((340)/(340-V_(S)))-680((340)/(340+V_(S)))=2`
`680xx340xx[((340+V_(S))-(340-V_(S)))/((340)^(2)-V_(S)^(2))]=2`
`implies (680xx340xx2V_(S))/((340)^(2)-V_(S)^(2))=2`
`V_(S) lt lt 340 implies (680xx340xx2V)/((340)^(2))=2 implies V_(S)=(340)/(680)=1/2 m//s`.