1) A large water tank has many corks bobbing on its surface. A simple wave propa

Question

1) A large water tank has many corks bobbing on its surface. A simple wave propagates from one end of the tank to the other. It is observed that the corks bob on the water with a maximum vertical speed of 3 cm/s and a maximum vertical acceleration of 2 cm/s2. (a) What is the amplitude of this water wave? (b) It is observed that a given row of corks at their maximum height (corresponding to a crest of the wave) are 3m away from the next crest of corks. What is the speed of propagation of the wave?

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Explanation / Answer

a.

maximum vertical speed = wA = 3
maximum vertical acceleration = (w^2)*A = 2
so,
(wA)^2 / (w^2)*A = 9/2
=>A = 4.5cm

b)

also,
wA = 3
so,
w = 3/4.5 = 0.67rad/sec,
f = w/(2*pi) = 0.106 Hz
here

wavelength/4 = 3

=> wavelength = 12m

so,

v = f*wavelength = 0.106*12 = 1.273 m/sec

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