The North Korean Navy decides that blue whales are getting in the way of their s

Question

The North Korean Navy decides that blue whales are getting in the way of their secret nuclear submarine base at a depth of 1.00 km below sea level. They plan to use sound to build up a resonance at the fundamental frequency in the whale and aggravate it until it leaves. Model a blue whale as a closed-closed cylindrical cavity 60' long times 10' diameter, filled with Water. What frequency should the NK's use? If the whale was wearing a an underwater microphone on a tracking collar then (assuming it was sensitive enough, low noise, ...) could a human biologist listening to the audio telemetry hear the sound (Explain). If they did, they would presumably report the incident to the UN commission animal abuse.

Explanation / Answer

speed of sound at 1 km depth in ocean, v =1485 m/s
length of cylinder, l = 60' = 18.288 m
diameter of cylinder, d = 10 ft

4. so a closed closed cylinder of length l has natutal frequency, f = v/lambda
but in closed closed case, lambda = 2l, l ,2l/3, .. 2l/n ( n = 1,2,3,)
so, f = nv/2l = n*1485/18.288*2 = 40.60039n
for fundamental frequency, n = 1, so f = 40.6 Hz

5. as this frequency in the human hearing range, if sound is amplified at the recieving station, the researchers can hear it and can apply to the international tribunal of UN commision for animal abuse

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