Question

A point source generates sound at constant frequency $f_0$. An observer is moving at a constant speed along the line as shown in the figure and the nearest distance of approach is at time $t_0$. The frequency of sound as heard by the observer can be best depicted as

• A. curve P.
• B. curve Q.
• C. curve R.
• D. curve S.

Answer 1

The correct option is C curve R.

$v_o$=speed of observer along the line shown. and $\theta$=angle between line joining source and observer and velocity.

Now, frequency observed by him

$f=\frac{v_s+v_o\cos \theta }{v_s}{f}_o$

where, $v_s$=speed of sound, $f_o$=frequency of sound as emitted by source and $v_o\cos \theta$=speed of observer towards source.

When, observer is very far from source $\theta \to 0$

$⟹f=\frac{v_s+v_o}{v_s}{f}_o$

When observer is direct in front of source, $\theta =\frac{\pi }{2}$

$⟹f=f_o$

When observer is again far away and going away from source, $\theta \to \pi$

$⟹f=\frac{v_s-v_o}{v_s}{f}_o$

Hence, we see that frequency decreases continuously as $\cos \theta$ decreases continuously.

Hence, the correct frequency curve as time passes is $R$.