This violation, of course, cannot happen. 00 W/m 2, which may appear to violate conservation of energy. 00 W/m 2, yet their sum has an intensity of 4. The two individual waves each have intensities of 1. The intensity goes up by a factor of 4 when the amplitude doubles. In fact, a wave’s energy is directly proportional to its amplitude squared because Because work W W is related to force multiplied by distance ( Fx Fx ) and energy is put into the wave by the work done to create it, the energy in a wave is related to amplitude. The larger the displacement x x, the larger the force F = kx F = kx needed to create it. More quantitatively, a wave is a displacement that is resisted by a restoring force. Large ocean breakers churn up the shore more than small ones. Loud sounds have higher pressure amplitudes and come from larger-amplitude source vibrations than soft sounds. Large-amplitude earthquakes produce large ground displacements. The amount of energy in a wave is related to its amplitude. Ultrasound is used for deep-heat treatment of muscle strains. Loud sounds pulverize nerve cells in the inner ear, causing permanent hearing loss. Earthquakes can shake whole cities to the ground, performing the work of thousands of wrecking balls. The energy of some waves can be directly observed. (credit: Petty Officer 2nd Class Candice Villarreal, U.S. The Richter scale rating of earthquakes is related to both their amplitude and the energy they carry. Figure 16.40 The destructive effect of an earthquake is palpable evidence of the energy carried in these waves.
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