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

Explanation

If n is the actual frequency , apparent frequency ` = n/2`
Here the listener is stationary, i.e., ` u_(o) = 0 `
Again decrease of frequency means that the source is receding from the listener . So the velocity of the source ` u_(s) ` is negative
Therefore, from the relation ` n. = (v + u_(0))/( v - u_(s))xx n ` , we have ,
` n/2 = (v)/(v + u_(s)) xx n " or " , v + u_(s) = 2v " or " , u_(s) = v `
i.e., the source is receding from the listener with the velocity of sound .