If a sound wave goes from a cold air region to a hot air region, its wavelength will?

Analyze the question: A sound wave moves from cold air into hot air. We need to know what happens to its wavelength.

Concept:

• The speed of sound in air increases with temperature. The speed is proportional to √T, where T is the absolute temperature in kelvin.
• When a wave crosses from one medium (or region) to another, its frequency stays constant. The frequency is set by the source.
• The wave equation is v = fλ, so λ = v/f.

Solution:

1. Cold air to hot air: the temperature rises, so the speed v increases.
2. The frequency f stays the same.
3. Since λ = v/f and f is constant, λ is directly proportional to v.
4. If v increases, then λ increases.

For example, at 0°C, v ≈ 331 m/s. At 30°C, v ≈ 349 m/s. For a 500 Hz sound:

• λ (cold) = 331/500 = 0.662 m
• λ (hot) = 349/500 = 0.698 m

The wavelength is longer in the hot air.

Answer: The wavelength will increase, which is option A.

Tip: Remember "Frequency is fixed, speed decides wavelength." When a wave enters a region where it travels faster (for sound, hotter air), the wavelength gets longer. When it enters a region where it travels slower, the wavelength gets shorter. Frequency never changes when a wave crosses a boundary.