When both source and observer approach each other with a speed equal to the half the speed of sound, then determine the percentage change in frequency of sound as detected by the listener.

Here we can use general formula of Doppler effect.fapp=fnv−vov−vs   ………(i)The direction of sound wave is always from source to observer. In this case both the source and observer are moving towards each other. The direction of motion of observer is opposite to the velocity of sound. So Eq. (i) becomesfapp=fnv−−vov−vs=fnv+vov−vsThe speed of source and observer is equal to half the speed of sound.Hence fapp=fnv+v2v−v2=3fnPercentage change in frequency% change =fapp −fnfn×100=3fn−fnfn×100=200%