Amplitude Physics Example 3

Follow the full solution, then compare it with the other examples linked below.

Example 3

medium

A wave on a string has amplitude

0.1 \text{ m}

and frequency

2 \text{ Hz}

. The string has a linear mass density of

0.05 \text{ kg/m}

and the wave speed is

10 \text{ m/s}

. What is the power transmitted by the wave? Use

P = \frac{1}{2}\mu\omega^2 A^2 v

Solution

1
Angular frequency: $\omega = 2\pi f = 2\pi \times 2 = 4\pi \text{ rad/s}$ .
2
Power: $P = \frac{1}{2}\mu\omega^2 A^2 v = \frac{1}{2}(0.05)(4\pi)^2(0.01)(10)$
3
$P = \frac{1}{2}(0.05)(157.9)(0.01)(10) = 0.395 \text{ W}$

Answer

P \approx 0.395 \text{ W}

The power carried by a wave depends on the square of both the amplitude and the frequency. Doubling the amplitude quadruples the power, which is why amplitude is so important in wave energy applications.

About Amplitude

The maximum displacement of a wave from its equilibrium (rest) position, measuring the wave's strength or intensity.

Learn more about Amplitude →

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A speaker produces a sound wave. The air molecules vibrate [formula] on either side of their equilib

Example 2 medium

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Example 4 hard

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