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WAEC Physics 2016 Paper

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Question : 29

Total: 47

The diagram given illustrates the waveform of a note produced by vibrations in an air column of length L. If the speed of sound in air is V, derive an expression for the frequency of the notes

$\frac{V}{L}$
$\frac{5VL}{2}$
$\frac{5L}{4V}$
$\frac{5V}{4L}$

Solution:

Concept:

The length of the air column is related to the wavelength of the standing wave, and the frequency is found from the wave equation

V = f\lambda

.

Explanation:

From the waveform shown, the length

L

represents

\frac{5}{4}

of the wavelength.

So,

L = \frac{5\lambda}{4}

.

Solving for wavelength:

\lambda = \frac{4L}{5}

.

Using the wave relation

V = f\lambda

, we get

f = \frac{V}{\lambda}

.

Substitute

\lambda = \frac{4L}{5}

:

f = \frac{V}{\frac{4L}{5}} = \frac{5V}{4L}

.

Answer:

f = \frac{5V}{4L}

— Option D.

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