(II) 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. Titus the speed υ (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 υ = Cg α h β λ γ , where α , β , γ , and C are numbers without dimension. ( a ) In deep water, the water deep below 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), determine the formula for the speed of surface waves in deep water. ( b ) In shallow water, the speed of surface waves is found experimentally to be independent of the wavelength (i.e.. γ = 0). Using only dimensional analysis, determine the formula for the speed of waves in shallow water.
(II) 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. Titus the speed υ (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 υ = Cg α h β λ γ , where α , β , γ , and C are numbers without dimension. ( a ) In deep water, the water deep below 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), determine the formula for the speed of surface waves in deep water. ( b ) In shallow water, the speed of surface waves is found experimentally to be independent of the wavelength (i.e.. γ = 0). Using only dimensional analysis, determine the formula for the speed of waves in shallow water.
(II) 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. Titus the speed υ (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 υ = Cgαhβλ γ, where α, β, γ, and C are numbers without dimension. (a) In deep water, the water deep below 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), determine the formula for the speed of surface waves in deep water. (b) In shallow water, the speed of surface waves is found experimentally to be independent of the wavelength (i.e.. γ = 0). Using only dimensional analysis, determine the formula for the speed of waves in shallow water.
When a sinusoidal wave crosses the boundary between two sections of cord as in Fig. 11–34, the frequency does not change (although the wavelength and velocity do change). Explain why
A stone dropped from the top of a tower of height 300 m splashes into the water of a pond near the base of the tower. When is the splash heard at the top given that the speed of sound in air is 340 m s-1 ? (g = 9.8 m s-2)
Standing waves can be said to be due to “interference inspace,” whereas beats can be said to be due to “interference in time.” Explain.
Chapter 15 Solutions
Physics for Scientists and Engineers, 4th Ed + Masteringphysics: Chapters 20-35
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