derive an expresson for the apparent frequency of the sound as heard by a stationary observer when the source is moving towards it?
Let the velocity of sound in still air be = vThe velocity of the source = a
The velocity of the observer = band the velocity of the medium (wind blowing) = w
Let Sl and Ol represent the positions of the source and the observer after 1 second. Distance travelled in 1 second is nothing but the velocity.
The waves produced by the source travel a distance SA in 1 second, but as the wind is blowing with a velocity w, it carries the wavefront from A to Al where A Al= w. The distance travelled by the waves relative to the source in 1 second.
If f is the frequency of the waves produced by the source, then f waves are accommodated in a distance SlAl.
Since the observer recedes by a distance b in 1 second, the relative velocity of the waves with respect to the observer is (v + w - b). Therefore, the apparent frequency is given by the number of waves of wavelength ll contained within the above distance.
Substituting for ll from equation (i), we get
Let us assume that the wind velocity is zero. Then w = 0 and b = 0. Equation (1-38) becomes
The apparent frequency will be greater than the actual frequency.