Wave Speed Homework: Find Frequency, Wavelength & Depth

[Jason17]

Homework Statement

Two fishing floats, a distance of 4.5 metres apart, bob up and down at 20 times per minute.
The floats always move in antiphase. There is always at least one wave crest between the floats but never more than two.

a) Show that the wavelength of the ripples on the river is 3.0 metres. Hence find the speed of the ripples on the surface

b) Near the bank, the depth of the river halves. The speed (v) of the water waves in shallow water of death (d) is given by v= √gd where (g) is 9.8 ms^-2
i) What is the new frequency and wavelength of the waves near the bank?
ii) What is the depth of the river near the bank?

Homework Equations

Velocity= frequency x wavelength

The Attempt at a Solution

I have tried for 45 mins straight to try and get to the answers.
For part a) i have absolutely no clue on how to show it is 3metres. I noted down that frequency is 20 ?

For part b) the equation i think is:
frequency = √gd / wavelength

3.13 x d
3
But that comes out with the wrong answer

Quite frustrated. That's all the information they've given me. I have the answers also but i don't know how to get there :s

Thanks in advance

 

[ideasrule]

Homework Statement

Two fishing floats, a distance of 4.5 metres apart, bob up and down at 20 times per minute.
The floats always move in antiphase. There is always at least one wave crest between the floats but never more than two.

a) Show that the wavelength of the ripples on the river is 3.0 metres. Hence find the speed of the ripples on the surface

Just imagine the situation. When one boat is at its lowest point, the other is at its highest, and there's one or two peaks in between them. Draw this out. What fraction of a wavelength is the distance between the boats?

b) Near the bank, the depth of the river halves. The speed (v) of the water waves in shallow water of death (d) is given by v= √gd where (g) is 9.8 ms^-2
i) What is the new frequency and wavelength of the waves near the bank?
ii) What is the depth of the river near the bank?

Frequency doesn't change; whatever vibration started the waves is still vibrating at the same frequency. v=frequency*wavelength, so if v halves, what happens to wavelength?