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SSC CGL Physics · Sound

Sound Waves and the Doppler Effect

The wave equation and what changes when sound moves from air into water, the Doppler effect, and the range of human hearing.

Why this matters

Seven questions in the bank: one from the 2024 shifts and six from the 2025 shifts. Four use the one equation v = f x wavelength, so learn it with the rule that frequency never changes between media.

Concept 1 of 2: The wave equation

Speed equals frequency times wavelength. The source fixes the frequency; the medium fixes the speed; so the wavelength adjusts.

Definition

The rules:

  • v = f x wavelength.
  • Frequency stays the same when sound passes from one medium to another.
  • Sound is faster in water (about 1,500 m/s) than in air (about 340 m/s), so going from air into water its wavelength grows.
  • Time = distance / speed.

Wave equation

v=fλv = f\lambda
  • vvSpeed of the wave
  • ffFrequency
  • λ\lambdaWavelength

Worked example

A sound of frequency 4 kHz has wavelength 8.5 cm. How long does it take to travel 1.7 km?
Practise this conceptself-check · 3 quick reps

The same idea in a real exam question:

SSC CGL · 2025 · Tier I, 16 Sep 2025, Shift 3 · Q43Easy

Example 1 · Sound · Sound Waves and the Doppler Effect

If the speed of sound in a medium is 340 m/s and a sound wave has a frequency of 680 Hz, what is its wavelength?

Faster medium, longer wavelength

Into water, speed and wavelength both increase. Options pairing a faster speed with a shorter wavelength are wrong.

Concept 2 of 2: The Doppler effect and hearing

A train's whistle sounds higher as it comes towards you and lower as it goes away. If source and listener move together, nothing changes.

Definition

Doppler effect:

  • The heard frequency changes with relative motion of source and listener: higher when they close in, lower when they separate.
  • Source and listener moving at the same speed in the same direction: no change.

Hearing: humans hear about 20 Hz to 20,000 Hz. Below is infrasound; above is ultrasound.

CaseHeard frequency
Train approachingHigher
Train moving awayLower
Both moving togetherUnchangedQ
Human hearing range20 to 20,000 HzQ
Practise this conceptself-check · 3 quick reps

The same idea in a real exam question:

SSC CGL · 2025 · Tier I, 14 Sep 2025, Shift 3 · Q42Easy

Example 2 · Sound · Sound Waves and the Doppler Effect

A person standing on a railway platform notices that the sound of an approaching train's whistle changes in pitch (frequency) as the train passes by. This phenomenon is best explained by:

No relative motion, no change

If source and listener move together at the same speed, the frequency does not change. Options saying it rises are wrong.

Summary — formulas & gotchas at a glance

A revision cheat-sheet for the formulas and gotchas above. Click any concept name to jump back to its full explanation.

Formulas (1)

Reference tables (1)

The Doppler effect and hearing4 rows
CaseHeard frequency
Train approachingHigher
Train moving awayLower
Both moving togetherUnchangedQ
Human hearing range20 to 20,000 HzQ

Watch out for (2)

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