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Question

A source of sound producing sound of frequency f is at rest. An observer starts moving toward it at t=0 with a constant small acceleration. Which of the following graph best represents the variation of observed frequency f′ recorded by the observer with time t?

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Solution

The correct option is **A**

After time t, velocity of observer,

v0=u+at=at

[observer starts from rest]

Now, observed frequency,

f′=(v+v0v−vs)f

⇒f′=(v+atv)f

⇒f′=(afv)t+f

This equation is similar to the equation of straight line, y=mx+c,

here,

Slope of straight line, m=afv and

y−intercept, c=f.

After time t, velocity of observer,

v0=u+at=at

[observer starts from rest]

Now, observed frequency,

f′=(v+v0v−vs)f

⇒f′=(v+atv)f

⇒f′=(afv)t+f

This equation is similar to the equation of straight line, y=mx+c,

here,

Slope of straight line, m=afv and

y−intercept, c=f.

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