Calculating Wave Velocity & Wavelength

[timtng]

A sound wave of velocity 600 m/s has a wavelength of 3 m. At a certain instant one of the molecules of the medium is at its normal position. How long will it be before this same molecule is again at its normal position?

v=fλ, f=v/λ =(600m/s)/3m = 200Hz
T=1/f=1/200=.005s

t=T/2 = .0025s Is this answer correct?

Thanks

 

[Ambitwistor]

Yes.

 

[timtng]

Another problem of the same sort.

Standing waves are produced on a string for which the velocity of transverse waves is 200 m/s. The frequency of vibration is 500 Hz. How far apart are the nodes?

I can only find λ, λ=v/f=200/500=.4m

I don't know how to finish the rest of the problem

 

[Ambitwistor]

That's like the previous problem. The nodes are the places where the transverse displacement of the string is zero, so they occur every half-wavelength.

 

[timtng]

So the answer should be λ/2?

 

[Ambitwistor]

Originally posted by timtng
So the answer should be λ/2?

Yes, that's what "half-wavelength" means.

 

[timtng]

shouldn't the answer be: L-λ/2

 

[Ambitwistor]

Originally posted by timtng
shouldn't the answer be: L-λ/2

No, why?

 

[timtng]

I figured since they ask how far apart are the nodes, L has to be a contributing factor.

 

[Ambitwistor]

Originally posted by timtng
I figured since they ask how far apart are the nodes, L has to be a contributing factor.

L will be some integer multiple of λ/2, but if you already know λ, it doesn't matter what L is. L just dictates how many nodes there are.

 

[HallsofIvy]

I figured since they ask how far apart are the nodes, L has to be a contributing factor.

Did you notice that there was no "L" given in the problem?

We were given, instead, the frequency.

If you were given the wavespeed (determined by the mass and tension of the string) and length, then you could find the frequency. Here, that's not necessary.