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Question:

A source of sound emits sound waves at frequency f0. It is moving towards an observer with fixed speed vs (vs<v, where v is the speed of sound in air). If the observer were to move towards the source with speed v0, one of the following two graphs (A and B) will give the correct variation of the frequency f heard by the observer as v0 is changed. The variation of f with v0 is given correctly by:

graph A with slope=f0(v+vs)

graph B with slope=f0(v+vs)

graph A with slope=f0(v−vs)

graph B with slope=f0(v−vs)

Solution:

f=f0(v+v0)/(v−vs)=f0(v−vs)v0+f0v/(v−vs)
where v is velocity of sound
As we see, this is of the formy=mx+c
slope m is:f0/(v−vs)