A sound wave traveling through air at a speed of 340\text{ m/s} has a wavelength of 0.85\t… — JAMB UTME

A sound wave traveling through air at a speed of $340\text{ m/s}$ has a wavelength of $0.85\text{ m}$ . Upon entering a second gaseous medium, its speed decreases to $272\text{ m/s}$ . What is the wavelength of the wave in the second medium?

$0.68\text{ m}$ Answer
B
$1.06\text{ m}$
C
$0.85\text{ m}$
D
$0.54\text{ m}$

Answer

The wavelength of the wave in the second medium is

0.68\text{ m}

Because wave frequency is determined by the source, it stays constant at

400\text{ Hz}

across both media. Using

\lambda_2 = \frac{v_2}{f}

, the wavelength in the second medium is

\frac{272\text{ m/s}}{400\text{ Hz}} = 0.68\text{ m}

Step-by-Step Solution

Calculate the frequency of the wave in the first medium using the wave equation

v = f \lambda

f = \frac{v_1}{\lambda_1} = \frac{340\text{ m/s}}{0.85\text{ m}} = 400\text{ Hz}

The source determines the wave frequency, which remains unchanged when passing into a new medium.

Apply the wave equation with the constant frequency to find the new wavelength in the second medium.

\lambda_2 = \frac{v_2}{f} = \frac{272\text{ m/s}}{400\text{ Hz}} = 0.68\text{ m}

Wave speed changes in a new medium lead directly to proportional changes in wavelength since frequency is constant.

Key Concept

Invariance of wave frequency across media boundaries and application of the wave equation

v = f \lambda

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