Q.When sound enters water from air or vice-versa, which physical quantity of the waves remains unchanged?

The key idea is that frequency is determined by the source and never changes when a wave enters a new medium, while wavelength scales with the wave speed. Here the speed reduces by a factor of 2, so the wavelength is halved — making option (C) correct.

Frequency of light is fixed by the source and never changes on reflection or refraction.

The frequency of a light wave is determined by the source that produces it, not by the medium it travels through. On reflection and refraction only the wavelength and speed change (since $v=f\lambda$ and $v$ depends on the medium); the frequency …

Frequency is fixed by the source and never changes on refraction; since $v = f\lambda$ and $v$ decreases in a denser medium, $\lambda$ must decrease too.

When a wave crosses from a rarer to a denser medium:

• Frequency is determined only by the source that generates the wave and stays the same in every medium — this is why frequency is used to define colour of light, unlike wavelength.
• Speed decreases in a denser medium because the refractive index $n = c/v$ is larger there, so $v = c/n$ is smaller. …

On crossing a boundary between media, frequency (fixed by the source) stays the same; wavelength changes because speed changes.

When light passes from one medium to another, its frequency $\nu$ is determined by the source and does not change. However, its speed $v$ changes because it depends on the refractive index of the medium ($v=c/n$). Since $v=\nu\lambda$, a change in speed at constant frequency means the wavelength …

Frequency is fixed by the source and stays unchanged as a wave crosses into a new medium; velocity and wavelength both change together via v = fλ.

For a wave $v = f\lambda$:

• Velocity (v) depends on the properties of the medium (elasticity/density for mechanical waves, permittivity/permeability for EM waves) — it changes when the wave enters a new medium.
• Wavelength (λ) depends on both the medium (through v) and the frequency, since $\lambda = v/f$ — so it changes whenever v changes. …

Frequency is fixed by the source and unaffected by the medium; energy per photon depends only on frequency.

When monochromatic light travels from a rarer to a denser medium, its speed decreases ($v=c/n$) and its wavelength decreases proportionally ($\lambda = \lambda_0/n$), but its frequency stays exactly the same, since frequency is determined by the source of the light, not by the medium through which it travels. Since the energy carried by each photon of the wave is $E=h\nu$, and $\nu$ is unchanged, the energy per photon (and hence the energy carried by the wave, ap …

Frequency stays fixed on refraction; since glass is optically denser, speed and hence wavelength decrease.

…

Frequency of a wave is determined by the source producing it and does not change when the wave crosses into a different medium - only wave speed and wavelength change (since v = f lambda, with f fixed).

When a sound wave refracts from air into water:

• The speed of sound changes (it is faster in water, ~1480 m/s, than in air, ~340 m/s), because speed depends on the elastic and inertial properties of the medium (bulk modulus and density).
• Since v = f lambda and v changes while f is fixed, the wavelength must also change (it increases when the wave enters the faster medium, water).
• The wave number k = 2 pi/lambda is inversely related to wavelength, so it changes too. …

Frequency is fixed by the source and can't change on crossing a boundary; since $v=f\lambda$ and $v$ falls in the denser medium, it must be $\lambda$ that shrinks.

Reasoning

When light passes from one medium to another, its frequency remains unchanged (it is set by the source and must match on both sides to keep the wave continuous at the boundary). Since

$v = f\lambda$

…

When light crosses from a rarer to a denser medium its frequency is unchanged (set by the source), but its speed falls, so its wavelength must also fall.

When a light wave travels from air into glass:

1. The frequency v of the wave is determined by the source and does NOT change on refraction — it stays the same in both media.
2. The speed of light in glass (v_glass = c/n, where n > 1 is glass's refractive index) is LESS than its speed in air. …