The audible Doppler effect for sound waves is observed when a source of sound moves in what way relative to the listener?

Introduction / Context:
The Doppler effect is a well known phenomenon in wave physics and everyday life. You hear it when an ambulance or train passes by and the pitch of the siren seems to change as it approaches and then moves away. This question focuses on when the Doppler effect occurs for sound waves, specifically in terms of the motion of the sound source relative to the listener.

Given Data / Assumptions:

• We are considering sound waves propagating through air.
• The listener is at rest in the medium, while the source of sound may move.
• We assume standard conditions: uniform medium and speeds much less than the speed of sound.
• We want to know for which directions of source motion the Doppler effect is observed.

Concept / Approach:
The Doppler effect arises whenever there is relative motion between the source and the observer along the line joining them. This relative motion changes the frequency of wave fronts that reach the observer compared with the frequency emitted. If the source moves towards the observer, wave fronts are compressed and the observed frequency increases, producing a higher pitch. If the source moves away, wave fronts are stretched and the observed frequency decreases, producing a lower pitch. Thus, the effect occurs for both approaching and receding motion, not just one direction.

Step-by-Step Solution:
Step 1: Imagine a sound source emitting waves at a constant frequency while stationary. The listener hears the original frequency without shift. Step 2: Now let the source move towards the listener. Successive wave fronts are emitted from positions closer to the listener, effectively reducing the spacing between them in front of the source. Step 3: Reduced spacing between wave fronts corresponds to a shorter wavelength, and because the speed of sound in air is nearly constant, the frequency heard by the listener increases. Step 4: If the source moves away from the listener, the opposite happens. Wave fronts are emitted from positions farther away, increasing the spacing and thus the wavelength, so the observed frequency decreases. Step 5: In both cases, approaching and receding, there is a change between emitted and observed frequencies, meaning the Doppler effect occurs whenever there is relative motion along the line of sight.

Verification / Alternative check:
Real life examples confirm this explanation. When a siren approaches, you hear a higher pitched sound, and as it passes and moves away, the pitch drops suddenly. Similar effects occur with moving trains or vehicles. Physics formulas for Doppler shift for a moving source provide separate expressions for motion towards and away from the observer, but both show a non zero frequency shift whenever relative motion is present. No shift occurs only when source and observer are at rest relative to each other along the line of propagation.

Why Other Options Are Wrong:
Away from the listener only: This includes only the case of receding motion and ignores the increase in pitch when the source approaches. Towards the listener only: This covers only the approaching case and ignores the frequency decrease when the source recedes. When there is no relative motion between source and listener: In that case, there is no Doppler shift, so this does not describe when the effect occurs.

Common Pitfalls:
Some learners incorrectly think that the Doppler effect only applies when the source moves towards the observer, because the higher pitch is more dramatic. Others forget that the listener can also move and create a similar effect. The key idea is relative motion along the line of sight. As long as there is such motion, whether the source moves, the observer moves, or both move, there will be a Doppler shift in the observed frequency.

Final Answer:
The audible Doppler effect for sound is observed when the source moves either towards or away from the listener so that there is relative motion along the line joining them.