Question

How fast is a wave if its frequency is 744.5 Hz and it has a wavelength of 163.1 m?

Answer 1

Use the relationship, `v=nulambda` where,`nu` is the frequency of a wave with wavelength `lambda` moving with speed `v`,

Given, `lambda=163.1m,nu=744.5Hz`

So,`v=(163.1*744.5)=121427.95 ms^-1`

Answer 2

The velocity `~= 1.21*10^5 m/s`.

Explanation:

It helps to remember that the unit `Hz` is equivalent to `"cycles"/s`. This problem is an example of when that can be useful.

The wave travels 163.1 m in the time of 1 cycle. (Note: we give the name period and the symbol `T` to "time of 1 cycle".) Since the frequency is `744.5 "cycles"/s`, what is the period, `T`?

There are 744.5 cycles in 1 second. Therefore the period is

`T = (1 s)/744.5 = 0.001343 s`

OK, now we know that the time that passed while the wave traveled 163.1 m was 0.001343 s.

Velocity is calculated
`v = "distance traveled"/"time for that travel"`

That works for waves as well as runners, so

`v = (163.1 m)/(0.001343 s) = 121428 m/s ~= 1.21*10^5 m/s`

I hope this helps,
Steve