Physics Solution – Question 8

Solution to Question 8

1. Analysis of Wavefront Propagation

To understand the pattern of the sound rays, we first look at how the wavefronts behave in the presence of wind.

Let the velocity of the wind be $\vec{v}_w$ directed towards the left (negative x-direction).
$$ \vec{v}_w = -v_w \hat{i} $$

As the source emits sound, the spherical wavefronts expand radially. However, the entire medium (air) is moving to the left. Consequently, the spherical wavefronts drift to the left as they expand.

The center of a wavefront emitted at $t=0$ will not remain at the source position but will shift by a distance $d = v_w t$ to the left.
This results in a set of non-concentric (eccentric) spherical wavefronts, crowded on the right side and spread out on the left side.

Figure 1: Wavefronts drifting to the left due to wind, and sound rays bending to remain normal to them.

2. Trajectory of Sound Rays

The relationship between sound rays and wavefronts is fundamental:

Key Concept: Sound rays are always normal (perpendicular) to the wavefronts.

Since the wavefronts are drifting and shifting towards the left, the normals to these wavefronts will also change direction.

Conclusion

The drifting of the wavefronts causes the rays to deviate from their straight paths in still air. This pattern of bending corresponds to the diagram shown in Option (c).