Questions: Wavelength, Frequency, and Wave Speed

Question 1

A 440 Hz sound wave travels from air (343 m/s) into water (1480 m/s). What happens to its wavelength?

• A. It increases by a factor of about 4.3, because a higher wave speed at the same frequency requires a longer wavelength
• B. It stays the same, because wavelength — like frequency — is set by the source
• C. It decreases, because the denser medium compresses the wave spatially
• D. It increases, but so does frequency, so the wave speed ratio is preserved

Answer: (A)

Frequency is fixed by the source at 440 Hz and cannot change at the boundary. Wave speed is determined by the new medium: 1480 m/s in water. Since v = fλ, wavelength = v/f = 1480/440 ≈ 3.4 m, compared to 343/440 ≈ 0.78 m in air — about 4.3 times longer. Option B describes the most common misconception: students often think wavelength is 'set by the source' like frequency, but it is the quantity that adjusts when the medium changes. Option C is wrong because a faster medium lengthens, not compresses, the wavelength.

Question 2

Which quantity is determined by the source of a wave rather than by the medium through which it travels?

• A. Wavelength — the spatial period is fixed when the wave is emitted
• B. Wave speed — the source controls how fast the disturbance propagates
• C. Frequency — the source oscillates at a fixed rate that the medium cannot alter
• D. All three are fixed by the medium once the wave enters it

Answer: (C)

The source oscillates at frequency f, completing f cycles per second. A medium boundary cannot change this rate — it would require the medium to somehow speed up or slow down the source's vibration, which is physically incoherent. Wave speed is entirely determined by medium properties (density and elasticity for mechanical waves). Since v = fλ and v changes at the boundary while f stays constant, wavelength must adjust: λ = v/f. This is why light slows in glass (lower v) and its wavelength shortens, while frequency (and thus color) stays the same.

Question 3

When light passes from air into glass, its frequency stays the same but its wavelength shortens.

• T. True
• F. False

Answer: True

This is the direct consequence of v = fλ. Frequency is fixed by the source. Glass slows light (lower v than air). Since λ = v/f and f is constant, a smaller v forces a smaller λ. This wavelength change at the boundary is also the origin of refraction: the wavefronts bend because the wavelength changes on one side before the other.

Question 4

If you double the frequency of a wave while keeping the wave speed constant, the wavelength also doubles.

• T. True
• F. False

Answer: False

From v = fλ, if v is constant and f doubles, then λ = v/f must halve. Frequency and wavelength are inversely proportional at constant wave speed. A common error is treating them as independent quantities; v = fλ is a constraint that ties all three together.

Question 5

Why does wavelength (and not frequency) change when a wave crosses from one medium into another?

Model answer: Frequency is set by the source — the rate at which it oscillates — and a passive medium boundary has no mechanism to alter that rate. Wave speed, however, is a property of the medium (its density, stiffness, or electromagnetic constants), so it changes at the boundary. Since v = fλ and f is fixed, wavelength must adjust to satisfy the relation: λ = v/f. In a faster medium, wavelength is longer; in a slower medium, it is shorter.

The physical image is helpful: in one period T = 1/f, the source produces exactly one wavelength's worth of disturbance. If the wave is slower on the other side, those same crests are packed more closely together — shorter λ. The number of crests passing any point per second (f) hasn't changed, because the source is still generating them at the same rate.