Problem 1
Reading: 2.4.3
What is the physical interpretation of A+2 in equation 2.125?
Problem 2
The ideal waveguide in jkps has pressure-release boundaries. Another ideal waveguide is one in
which the top and bottom boundaries are rigid instead of pressure release. Discuss what you
think the mode shapes would be in this case. (hint: think of why the modes go to zero at the
boundaries of the waveguide in the pressure-release case. What must the modes look like near
the boundary to satisfy the rigid boundary conditions?)
Problem 3
Consider a 200 m waveguide, with pressure release boundaries and c=1500m/s
a) A whale at 100 m depth has a pressure level of 150 dB re 1µPa at 1 m.
What is the pressure level you receive at 10100m?
b) The noise at the receiver is 75 dB. What is the SNR (Signal to Noise Ration)
c) Processing with an array of hydrophone gives an array gain of 5dB. What is the array
SNR?
d) We have a detection threshold of 5 dB. What is the signal excess ? Can we observe the
whale?
Regarding 3a) the units is discussed in section COA 1.3.3 with more detail in the first few pages
of chapter 10. Thus
A1) 1micro Pascal =1µPa= 10-6Pa.
A2) “The pressure level of 150 dB re 1uPa at 1 m.” means
PdB(1m)=20log10[p(1m)/p0]=150
With p0=1µ Pa
Thus p(1m)= 10-6Pa *10150/20=103/2Pa=30Pa
A3)p(10km)=p(1m)*TLlin
