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the answer are a) 5.5*10^-4 and b) 1.1*10^-3,but i have no idea how to get that.

ID: 2245314 • Letter: T

Question

the answer are a) 5.5*10^-4 and b) 1.1*10^-3,but i have no idea how to get that.please show all work,thank you very much!

A sinusoidal plane wave of sound in air falls on a water surface at normal incidence. The speed of sound in air is about 334 m/s and the speed in water is about 1480 m/s. The density of air is about 1.225 kg/m3 at sea level, and the density of water is 1000 kg/m3. The appropriate boundary conditions for longitudinal waves are continuity of wave displacement and wave pressure. The latter is given by K( xi/ x), where K is the bulk modulus of the medium. (This follows from Delta p = -K Delta V/V = -K Delta xi/Delta x.) Since the wave speed v is given by (K/rho)1/2, the reflection and transmission coefficients are expressible in terms of rho and v only. What is the amplitude of the sound wave that enters the water, expressed as a fraction of the amplitude of the incident wave? What fraction of the incident energy flux enters the water?

Explanation / Answer

b) flux entering water/incident flux=coefficient of transmissiion=4Z1*Z2/(Z1+Z2)^2

here Z1,Z2 are acoustic impedence of material

Z1(air)=1.225*334=409.15

Z2(water)=1480*1000=1480000

coefficient of transmissiion=4*409.151480000/(1480409.15)^2

=0.001105

a)=2*Z1/Z2

=2*409.15/1480000 =5.52*10^-4