What should be the velocity of a listener so that the apparent frequency of the sound coming from a stationary source to him will be twice the actual frequency ? Velocity of sound in air = v .

Explanation

Apparent frequency, n. = (v = u_(o))/( v - u_(s)) xx n `
In this case apparent frequency higher , the listener is approaching the source, i.e., velocity of the listener ` u_(o)` is positive . Again, ` n. = 2n ` .
` therefore 2n = (v+ u_(o))/(v) xx n " or " , 2v + v + u_(o) " or " , u_(o) = v `
i.e., the listener is approaching the stationary source with the velocity of sound .