Amplitude Physics Example 4

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Example 4

hard
A seismograph records an earthquake wave with amplitude 2 mm2 \text{ mm}. A second earthquake produces waves with 44 times the energy. What is the amplitude of the second earthquake's waves?

Solution

  1. 1
    Wave energy is proportional to the square of amplitude: E∝A2E \propto A^2.
  2. 2
    If E2=4E1E_2 = 4E_1, then A22=4A12A_2^2 = 4A_1^2, so A2=2A1A_2 = 2A_1.
  3. 3
    A2=2×2=4 mmA_2 = 2 \times 2 = 4 \text{ mm}

Answer

A2=4 mmA_2 = 4 \text{ mm}
Since wave energy scales with the square of amplitude, quadrupling the energy only doubles the amplitude. This squared relationship between energy and amplitude applies to all types of waves.

About Amplitude

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

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