Question

A source of sound emits sound waves at frequency \( f_0 \). It is moving towards an observer with fixed speed \( v_s \) (\( v_s < v \), where \( v \) is the speed of sound in air). If the observers were to move towards the source with speed \( v_0 \), one of the following two graphs (A and B) will give the correct variation of the frequency \( f \) heard by the observer as \( v_0 \) changes.

• A. Graph A with slope \( \frac{f_0}{v + v_s} \)
• B. Graph B with slope \( \frac{f_0}{v - v_s} \)
• C. Graph A with slope \( \frac{f_0}{v - v_s} \)
• D. Graph B with slope \( \frac{f_0}{v + v_s} \)

Hint:

For moving sources and observers, the Doppler effect formula is critical for understanding frequency shifts. Pay attention to the relative speeds involved.

Answer 1

The Correct Option is C

The Doppler effect equation for frequency heard by an observer moving towards a source is given by: \[ f = f_0 \frac{v + v_0}{v - v_s} \] This formula indicates that the frequency \( f \) increases as the observer approaches the source. The slope of the graph \( f \) with respect to \( v_0 \) (observer’s speed) is: \[ \text{slope} = \frac{f_0}{v - v_s} \] Thus, graph A is the correct choice.