A progressive transverse wave with a frequency of 50\text{ Hz} travels through a medium wi… — JAMB UTME

A progressive transverse wave with a frequency of $50\text{ Hz}$ travels through a medium with a wave speed of $300\text{ m/s}$ . If the wave crosses a boundary into a second medium where its speed decreases to $150\text{ m/s}$ , what is the frequency of the wave in the second medium?

$50\text{ Hz}$ Answer
B
$25\text{ Hz}$
C
$100\text{ Hz}$
D
$75\text{ Hz}$

Answer

The frequency of the wave in the second medium is

50\text{ Hz}

The frequency of a wave is determined entirely by the vibrating source that creates it. When a wave passes from one medium to another, its speed and wavelength change, but its frequency remains constant. Therefore, the frequency remains

50\text{ Hz}

Step-by-Step Solution

Identify the given physical parameters.

Initial frequency

f_1 = 50\text{ Hz}

, initial speed

v_1 = 300\text{ m/s}

, new speed

v_2 = 150\text{ m/s}

Recognize which wave properties are given and which property is being asked for.

Apply the fundamental principle of wave propagation across different media boundaries.

Frequency

f

depends only on the source of vibration and remains constant during refraction/transmission across media boundaries.

While wave speed

v

and wavelength

\lambda

change when entering a new medium, frequency

f

remains unaffected.

Determine the frequency in the second medium.

f_2 = f_1 = 50\text{ Hz}

Since frequency is invariant across media boundaries,

f_2

must equal

50\text{ Hz}

Key Concept

Invariance of wave frequency across media boundaries

Estimated Time:45s

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