A transverse wave of frequency 15\text{ Hz} propagates from a dense medium where its speed… — JAMB UTME

A transverse wave of frequency $15\text{ Hz}$ propagates from a dense medium where its speed is $45\text{ m s}^{-1}$ into a lighter medium where its speed decreases to $30\text{ m s}^{-1}$ . What is the frequency of the wave in the second medium?

A
$10\text{ Hz}$
$15\text{ Hz}$ Answer
C
$22.5\text{ Hz}$
D
$2.0\text{ Hz}$

Answer

The frequency of the wave in the second medium is

15\text{ Hz}

The correct answer is

15\text{ Hz}

because the frequency of a wave is determined solely by the source that creates it. When a wave passes from one medium into another, its speed and wavelength change proportionally, but the frequency remains constant.

Step-by-Step Solution

Identify the property of a wave that is source-dependent and invariant across boundaries.

The frequency (

f

) of a wave is determined entirely by the oscillating source generating the wave.

When a wave crosses the boundary between two different media, its speed (

v

) and wavelength (

λ

) change due to the properties of the new medium, but its frequency (

f

) remains constant.

Determine the frequency in the new medium.

f_{\text{second medium}} = f_{\text{initial}} = 15\text{ Hz}

Since frequency does not change across medium boundaries, the wave maintains a frequency of

15\text{ Hz}

Key Concept

Invariance of Wave Frequency Across Media Boundaries

Estimated Time:45s

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