Waves: Conceptual Doubts Cleared (2)

medium 3 min read
Tags Waves

Question

When a sound wave passes from air into water, which of the following changes — frequency, wavelength, or speed? Most students freeze at this question. Let’s settle it once and for all.

Solution — Step by Step

Frequency is set by the source of the wave (vocal cords, tuning fork, speaker). The source vibrates at a fixed rate, and each crest leaving the source must arrive at the receiver at the same rate — otherwise crests would pile up or vanish, which is impossible.

So frequency stays constant across media.

Wave speed depends on the medium’s properties — bulk modulus and density for sound:

v=B/ρv = \sqrt{B/\rho}

Water has higher bulk modulus than air, and although it is denser, the bulk modulus increases more dramatically. Sound travels at 1500m/s\sim 1500 \, \text{m/s} in water vs 340m/s\sim 340 \, \text{m/s} in air.

So speed changes when the medium changes.

The relation v=fλv = f\lambda must hold in every medium. Frequency is fixed, speed changes, so wavelength must change in the same ratio as speed.

Going air → water: λ\lambda increases by ~4.4× (since speed increases by ~4.4×).

Frequency: unchanged. Speed: changes. Wavelength: changes.

Why This Works

This is one of those questions where the textbook formula v=fλv = f\lambda does the heavy lifting — we just need to know which variable is locked.

Think of it like a rope of people passing balls: the person at one end (source) hands off balls at a fixed rate. The rate at which balls reach the other end must match the input rate, regardless of how stretchy the rope is.

The “stretchiness” determines how fast each ball moves and how spaced apart they are — but not the rate at which they leave the source.

Alternative Method — Boundary Condition Argument

At the air-water interface, particles on both sides oscillate together (they cannot separate or overlap). So the time period of oscillation must match — which means frequency matches.

This gives a more rigorous reason than “the source determines frequency”: even if you tried to force different frequencies, the boundary would refuse.

Memory hook: “Source sets frequency, medium sets speed, wavelength adjusts.” This applies to sound, light, and any mechanical or EM wave going across boundaries.

Common Mistake

Students often say wavelength stays the same because “the wave is the same.” This confuses the wave’s identity (its frequency) with its spatial pattern (its wavelength).

Another trap: thinking speed stays the same because “speed is a property of the wave.” Wrong — wave speed is a property of the medium for mechanical waves and of μ0ϵ0\mu_0\epsilon_0 for EM waves in vacuum. Both depend on what the wave is travelling through.

NEET 2021 asked a similar question about light going from air to glass. Students who picked “frequency changes” lost 4 marks plus negative marking. The correct logic: frequency stays the same, speed decreases (since n>1n > 1), wavelength decreases proportionally.

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