What happens to the perceived frequency when both the source and the listener move with the same speed in the same direction?

Correct — C. The Doppler effect depends on relative motion between source and listener, not on how fast each moves over the ground.

Same speed, same direction: the gap between them never changes.
Source behind the listener, both at speed u through still air (speed of sound v):
f′ = f × (v − u)⁄(v − u) = f

The perceived frequency equals the source's own frequency → option (c).

Why the others are wrong

• (a)
  It increases — It increases only when the gap is closing, with source and listener approaching. Moving together at the same speed, the gap never shrinks.
• (b)
  It decreases — It decreases only when the gap is growing, with source and listener moving apart. Here neither pulls away from the other.
• (d)
  It fluctuates rapidly — Fluctuation would need the relative speed to keep changing. Both speeds are equal and steady, so the heard frequency is steady too, and equal to the source's.

The Doppler effect is the change in frequency a listener hears when source and listener move relative to each other. Approach raises the pitch, and moving apart lowers it.

For sound in still air, f′ = f × (v ± vₒ)⁄(v ∓ vₛ), where v is the speed of sound, vₒ the listener's speed and vₛ the source's. The upper signs apply when each moves towards the other. Equal speeds in the same direction cancel.

Key facts

• Christian Doppler proposed the effect in 1842.
• Approaching each other raises the heard frequency, and moving apart lowers it.
• With no relative motion between source and listener, the heard frequency equals the emitted frequency.
• Radar speed guns, Doppler ultrasound of blood flow and astronomical redshift all use the Doppler effect.

Common traps

• Answering 'increases' because both are moving. Only the relative motion counts.
• Adding the two speeds. Equal speeds in the same direction give zero relative speed.

No directly related past PYQ was found.