A water wave traveling in deep water has a wavelength of 0.80\text{ m} and a speed of 2.4\… — JAMB UTME

A water wave traveling in deep water has a wavelength of $0.80\text{ m}$ and a speed of $2.4\text{ m/s}$ . Upon entering a shallow region, its speed drops to $1.8\text{ m/s}$ . What are the frequency and wavelength of the wave in the shallow region?

Frequency = $3.0\text{ Hz}$ , Wavelength = $0.60\text{ m}$ Answer
B
Frequency = $2.25\text{ Hz}$ , Wavelength = $0.80\text{ m}$
C
Frequency = $2.25\text{ Hz}$ , Wavelength = $0.60\text{ m}$
D
Frequency = $0.33\text{ Hz}$ , Wavelength = $0.60\text{ m}$

Answer

Frequency =

3.0\text{ Hz}

, Wavelength =

0.60\text{ m}

When a wave passes from deep to shallow water (refraction), its frequency remains unchanged because frequency is fixed by the source. Using

v = f\lambda

, the initial frequency is

f = \frac{2.4}{0.80} = 3.0\text{ Hz}

. In shallow water, the new wavelength is

\lambda' = \frac{1.8}{3.0} = 0.60\text{ m}

Step-by-Step Solution

Calculate the frequency of the wave in deep water using the wave equation

v = f \lambda

f = \frac{v}{\lambda} = \frac{2.4\text{ m/s}}{0.80\text{ m}} = 3.0\text{ Hz}

The frequency depends on the wave source and can be determined from the given initial speed and wavelength.

Apply the boundary condition for wave refraction.

The frequency in shallow water remains

f = 3.0\text{ Hz}

When a wave travels from one medium to another, its frequency remains constant.

Calculate the new wavelength in shallow water using

\lambda' = \frac{v'}{f}

\lambda' = \frac{1.8\text{ m/s}}{3.0\text{ Hz}} = 0.60\text{ m}

The wavelength changes proportionally with speed when frequency is constant.

Key Concept

Constancy of wave frequency during refraction across medium boundaries

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