Question

a. Find an approximate formula for the speed of a wave on the surface of the deep ocean. Your answer may involve mass density of water, wavelength of the wave, and/or acceleration of gravity, nor does the surface tension of the water.

b. Then evaluate the answer numerically for a wavelength of one meter.

Answer 1

(a) The speed of wave is wavelength of the wave in a timeperiod .

As we know speed= distance/time . So in case of wave we can say speed =wavelength/ time (since distance = wavelength)

Now as we know 1/time= frequency(f)

Therefore we can say speed= wavelength*frequency

Now we can write it as v=f*l (l=wavelength)

Now as we go deep the speed of wave can be written as v=√(gl/2π) where g is accleration due to gravity which is 9.8. so the value of v is v= √(9.8*l/2*3.14) where (π=3.14)

V=1.25√l approx

If depth is given then this formula can be written as. V=√gd where d = depth and g= 9.8m/s²

b) as given wavelength l=1m

Then we know V=√(gl/2π)

V=√(9.8*1/2*3.14)

V=1.249m/s