Wavelength Ratios for a Pitching Boat in a Deep Lake

[songoku]

Homework Statement

It is known that a water wave in a lake produced by the pitching of a boat at anchor with a pitching period T propagates with a speed bT ( b > 0) if the lake is deep enough and the water is at rest. Assume that a boat moves at a slow constant speed Vo with a pitching period T.

a. Find (wavelength in the forward direction / wavelength at rest) in terms Vo and bT
b. Find (wavelength in the backward direction / wavelength at rest) in terms Vo and bT

Homework Equations

$$V = \lambda f$$

The Attempt at a Solution

What is the meaning of pitching of a boat at anchor?
Is pitching period the same as the usual period?

thx

 

[negitron]

Pitching is another term for rocking back and forth. At anchor means, well, that the anchor is down, constraining the boat from drifting. Consider the pitching boat to be functionally equivalent to moving a submersed plunger up and down in the water; each cycle of the plunger will produced one wavelength. You need not read any more into it than that for this problem.

That help?

 

[songoku]

reallly help ^^

I suppose wavelength at rest = v / f = vT = b T^2

Wavelength in forward direction = (bT - Vo) T ?
If i make a new reference where the speed is at rest, the speed of the wave will be (bT - Vo) ??

thx

 

[rl.bhat]

Here the source of wave is rocking boat. The velocity of the wave in the water is bT.
When the boat moves with constant velocity Vo, wavelength in the forward direction is shortened. The expression you have written is correct.
In the backward direction the wavelength will be increased and it will be expressed as
(bT + Vo)T

 

[songoku]

I really appreciate your help

thx a lot rl.bhat and negitron ^^