How Do You Calculate Frequency from Wave Loops and Travel Time?

[ElegantSir]

A string has one end tied to a wave generator, and the other tied to a fixed position,. It takes the wave 0.10 seconds to travel 4.5m. Withing the same distance there are 3 complete loops. Find the frequency of the source.

Pretty generic question. But I keep getting stuck at trying to find the number of cycles to find the frequency. I've found the wavelength, which is 3 meters. I made an educated guess at saying there were 1.5 cycles seeing as the equation said there were 3 complete loops. If I am wrong I would appreciate any help possible. Cheers!

 

[andrewkirk]

The word 'loop' is unhelpful. Is that what the question said?

My guess is that it means three complete full waveforms, ie three consecutive wavelengths of a sinusoidal shape. If that's correct then the wavelength is one third of the distance. Now you have the wave speed and the wavelength so you can use the usual equation to calculate the frequency.

 

[ElegantSir]

The equation did in fact use the word "loop." I am not too sure I understand where you are going with this though. The known factors thus far are:
t = 0.10 seconds
d = 4.5m
f = ?

I calculated the wavelength using this equation. λ / 2 = # of loops
3λ / 2 = 4.5
1.5λ = 4.5
λ = 4.5 / 1.5
λ = 3 meters Therefore wouldn't the wavelength equal 3 meters?

And even then to find the frequency I would have to use v = fλ where I only know the wavelength and nothing more.

 

[Joshua Kenny]

To calculate the frequency from the given data, this simple formula should do it:

$f=\frac{n}{t}$

where :
n = the number of (complete) waves that propagated [wave(s)]
t = the time period [second(s)]

The number of waves itself isn't clear since the meaning of the word 'loop' is vague. Anyway, try plugging in the values into that formula and you should get the value of the frequency.

 

[ehild]

I calculated the wavelength using this equation. λ / 2 = # of loops
3λ / 2 = 4.5
1.5λ = 4.5
λ = 4.5 / 1.5
λ = 3 meters Therefore wouldn't the wavelength equal 3 meters?

And even then to find the frequency I would have to use v = fλ where I only know the wavelength and nothing more.

It is also given that

It takes the wave 0.10 seconds to travel 4.5m.

 

[andrewkirk]

I calculated the wavelength using this equation. λ / 2 = # of loops

Where did you get that equation? If it came from your lecturer then it implies that by 'loop' she means half of a full waveform. It is non-standard terminology so solution of the problem depends entirely on what she means by that word. If she does mean half a waveform then indeed the wavelength will be the 3m that you guessed.
Regarding the value of v, look at ehild's post.

 

[victorhugo]

This is how I got taught to find V, f & λ here in Australia, hopefully by giving you a slight different view on this you can wrap your head around it more...

We don't need the wavelength to find the frequency here, we need to figure out the period (time it takes the wave to make one complete CYCLE) since there are 3 complete cycles, and it took 0.10 seconds for 3 of them to form, 1 cycle must have taken 0.10 / 3 = 0.0333333 seconds. That is the period, T, and frequency is = 1/T , 1/0.0333 = 30Hz. To do it in one equation you could just do 1 / (0.10/3) = 30Hz.

If you were to get the velocity you would need frequency and wavelength,λ, as V=fλ. When there were 3 complete loops, there were 3 complete wave forms as i state above (when it forms a trough and a crest and goes back to the middle line) so there are 3 troughs and crests, the wavelength is the length between those... so it must be 1/3 of the distance, 4.5m / 3 = 1.5. therefore λ= 1.5m
V= f x λ
V= 30 x 1.5
V= 45 m/s