A water wave with a frequency of 20\text{ Hz} and a wavelength of 0.60\text{ m} in deep wa… — JAMB UTME

A water wave with a frequency of $20\text{ Hz}$ and a wavelength of $0.60\text{ m}$ in deep water enters a shallow region where its speed becomes $8.0\text{ m s}^{-1}$ . What is the wavelength of the wave in the shallow region?

$0.40\text{ m}$ Answer
B
$0.60\text{ m}$
C
$0.90\text{ m}$
D
$1.50\text{ m}$

Answer

The wavelength of the wave in the shallow region is

0.40\text{ m}

When a wave passes from one medium into another, its frequency remains constant because frequency depends only on the source. Applying the wave equation

v = f\lambda

to the shallow region gives

\lambda = \frac{v}{f} = \frac{8.0\text{ m s}^{-1}}{20\text{ Hz}} = 0.40\text{ m}

Step-by-Step Solution

Identify the constant parameter during wave refraction.

The frequency of the wave remains

f = 20\text{ Hz}

Frequency is determined entirely by the source producing the wave and does not change upon entering a new medium.

Calculate the new wavelength using the wave equation

v = f\lambda

$\lambda = \frac{v}{f} = \frac{8.0\text{ m s}^{-1}}{20\text{ Hz}} = 0.40\text{ m}$.

Dividing the wave speed in the new medium by the constant frequency yields the wavelength in that medium.

Key Concept

Constancy of wave frequency during refraction across media boundaries

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