acoustics

  
Problem 1 Absorption coefficient 
Plot the combined classical absorption coefficient as a function of frequency (over an appropriate acoustic range) for both air and fresh water at 20◦ C. Discuss the results, including any assumptions you are making, and be sure to cite the source of your material parameters. Submit both the plots and a printout of your code (likely a .m file, but up to you). You will be graded on ability to run the script/function, correctness of solution, and legibility of code. 
Problem 2 Cavitation 
An sound transducer in a freshwater lake generates very intense sinusoidal plane waves in the water. If during the negative half cycle, the total pressure (ambient plus acoustic pressure) becomes zero, cavitation (the production of air bubbles) may occur. Recall that the ambient pressure at a depth h is given as h = p0 + ρ0gh, where p0 is the atmospheric pressure above the surface of the water, ρ0 is the water density, and g is the acceleration due to gravity. 
What is the maximum acoustic intensity that may be achieved without running the risk of cavitation at a transducer depth of 10 m? What is the SPL (re 1 μPa) that corresponds to this intensity? 
Problem 3 Finding a hidden sound source 
An omnidirectional point source of sound S is immersed in a freshwater lake. An observer on the shore notes that the sound in transmitted in the air at an angle of 5◦ (referenced to the vertical) at his current location. When he moves 1 m farther from the source, he notes that the angle has increased to 6◦. How far away was the observer from the source at his original location, and how deeply submerged is the source? (See Blackstock Problem 5-2 for a sketch of the geometry) 
Problem 4 Modes of a water tank 
A water tank of width W , length L, and height H has rigid ends and bottom, pressure release sides, and an open top.
(a) Find an expression for plmn, the pressure of the (lmn)th mode
(b) Find an expression for flmn, the frequencies of the normal modes. What are the allowed, non-trivial values of l, m, and n? 
(c) A tank of W =0.5ft,L=2ft,andH =1ftisfilledwithfreshwaterat20◦C. List the six lowest nontrivial modes and their indices in order of increasing frequency. 
Problem 5 Derive the conservation of mass for the three-dimensional acoustic wave equation 
Start with a small fluid element fixed in space. The change in mass in all three dimensions must equal the change in mass of the entire element. 

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