# Water waves

1. Mar 22, 2006

### Fermat

I got this question,

A wave with a frequency of 10 hertz moves at 360 m/s.
Part (a) What is the wavelength of the wave?
Part (b) What is the period of the wave?

I treated this as a deep water wave, and used the equations,

c2 = gl/(2pi)
w2 = gk
c = w/k

to find the wavelength and period of the wave.
But I never used the frequency given (which would imply a period of 0.1 sec) and instead got a period of 231 sec.

Is there something I'm missing?
Is it possible to solve the above question without using deep water equations?

2. Mar 22, 2006

### Staff: Mentor

I don't know what those equations mean, but why can't you use the simple relations between frequency, period, and wavelength? They are good for all waves, regardless of type because they are based on the very definitions of the words.

3. Mar 22, 2006

### Fermat

I wish I knew what the simple relations were, but those eqns I gave are the only ones I've come across when dealing with waves and the wave equation.

c = wave speed
l is lambda = wavelength
w is omega - angular frequency
k is the wave number

uh, what are the simple relations?

4. Mar 22, 2006

### Staff: Mentor

Think about it: the units of wavelength are distance. The units for frequency are distance over time. The units for period are just time. So if you have a distance over time and you multiply by a time, what do you get...?

5. Mar 22, 2006

### Fermat

Well, I can certainly manipulate T, f and w to give me
w = 2pi.f = 2pi/T
and carry out dimensional analysis etc, but i'm at a loss to see; how does that relate the wavelength to the wave speed in the original problem ?

6. Mar 22, 2006

### Staff: Mentor

2pi*f??? Where are you getting the 2pi? Wavelength is linear, speed is linear.

Through the dimensional analysis:

w=p*s
p=1/f

It really is that simple.

Last edited: Mar 22, 2006
7. Mar 22, 2006

### Fermat

I am using T as period.

f is frequency in cycles per second (cps)

one cycle is equivalent to one circular movement = 2pi radans, so f cps = 2pi.f radians per sec givng the angular frequancy as w = 2pi.f

Are you using p as period, yes? then p = 1/f is the same as my T = 1/f.

But how does the wavelength of a wave relate to its speed?

8. Mar 23, 2006

### Fermat

OK, sussed it out.
The frequency given in the problem above is the wave frequency and is the number of waves passing along the surface of the water (per unit time).
The frequency I had been working with was the number of times a wave rises and falls, vertically, in a unit time.

Problem solved.

9. Mar 23, 2006

### prsident21ct

Can you tell me what is the deep water wave equation?
Maybe we can discuss later.

10. Mar 23, 2006

### Staff: Mentor

What textbook are you using that doesn't have $v = f \lambda$ ?

:surprised:

11. Mar 23, 2006

### Staff: Mentor

Those are two different ways to describe the same measurement.