Estimate the average power of a moving water wave that strikes the chest of an adult standing in the water at the seashore. Assume that the amplitude of the wave is 0.50 m, the wavelength is 2.5 m, and the period is 4.0 s.

An earthquake-produced surface wave can be approximated by a sinusoidal transverse wave. Assuming a frequency of 0.60 Hz (typical of earthquakes, which actually include a mixture of frequencies), what amplitude is needed so that objects begin to leave contact with the ground? [Hint: Set the acceleration a > g. Why?]-

Dimensional analysis. Waves on the surface of the ocean do not depend significantly on the properties of water such as density or surface tension. The primary 'return force' for water piled up in the wave crests is due to the gravitational attraction of the Earth. Thus the speed v (m/s) of ocean waves depends on the acceleration due to gravity g. It is reasonable to expect that υ might also depend on water depth h and the wave's wavelength λ. Assume the wave speed is given by the functional form v = Cgᵅ hᵝ λᵞ, where α , β , c and C are numbers without dimension. In deep water, the water deep below the surface does not affect the motion of waves at the surface. Thus υ should be independent of depth h (i.e., β = 0). Using only dimensional analysis (Section 1–7 and Appendix D), determine the formula for the speed of surface ocean waves in deep water.

Two strings on a musical instrument are tuned to play at 392 Hz (G) and 494 Hz (B). What are the frequencies of the first two overtones for each string?

A transverse wave pulse travels to the right along a string with a speed v = 2.4 m/s. At t = 0 the shape of the pulse is given by the function D = 4.0m³ / (x² + 2.0m²), where D and x are in meters. Determine a formula for the wave pulse at any time t assuming the pulse is traveling to the left.