Wave Energy and Intensity Waves aves transfer energy from one location to another. As the wave propagates the particles in a dense elastic transmitting medium perform simple harmonic motion about their equilibrium positions. Wave Energy and Power Suppose each particle in the medium has a mass m and vibrates at a frequency with an amplitude A. If mechanical energy is conserved the total oscillatory energy of each particle: E=YKA where k is the elastic (spring) constant of the medium. The frequency of an object in simple harmonic motion: 2xVm Therefore, the elastic constant: k = 4x f'm and the total oscillatory energy of the particle: E = 2xmA If there are N identical particles per unit volume V in the medium, the total oscillatory energy per unit volume: =(2xmA)N Since each particle has a mass m, the density (total mass per unit volume): p = Nm Therefore, the total wave energy per unit volume (energy density): =2xp (17-9) Consider now the wave energy flow through a volume V of material in the medium that has a cross-sectional area A' and length (see Fig. 17-17)." Note: A is the wave amplitude, not an area. To distinguish amplitude from area we shall use A' for the area. 1. (4 pt) Consider the measurement of a tsunami's height. With a monitoring station 2.50 km away from the epicentre, we have recorded a wavefront with a height of 12.0 m. If we consider the wave to be spreading only at the surface (i.e., in 2D, not 3D), and ignore any dissipation, how high is the wave going to be at the shore, 70.0 km away? The amplitude of a wave is proportional to the square root of the intensity (see derivation in textbook 17-23)