How Do You Calculate the Propagation Speed of a Transverse Wave on a String?

[RavenBlackwolf]

< Mentor Note -- thread moved to HH from the technical physics forums, so no HH Template is shown >

A transverse wave on a string has an amplitude of 16cm, a wavenumber of 5.7m^-1, and a frequency of 39Hz. What is the propagation speed of that wave?
(a) 6.84 m/s
(b) 39.2 m/s
(c) 43 m/s
(d) 6.24 m/s
(e) 6.88 m/s
This is a question on my physics study guide packet and while we have done wave problems in the past it was never anything like this. First: can someone explain what a wavenumber is. Second: what is propagation speed. Third: which equation should I be using. I thought maybe x_mcos(ωt+Φ) but I don't know what the phase angle would be. I'm very confused, I would just like to have a basic understanding of what this is asking.

 

[davenn]

Hi there
welcome to PF

I have asked for this to be moved to homework section

A transverse wave on a string has an amplitude of 16cm, a wavenumber of 5.7m-1, and a frequency of 39Hz. What is the propagation speed of that wave?

from what you have studied so far, show us some of your thoughtsDave

 

[RavenBlackwolf]

Oh I didn't know there was one, sorry.

 

[BvU]

In particular: do you have an expression for the speed of a wave on a string ?

 

[RavenBlackwolf]

In particular: do you have an expression for the speed of a wave on a string ?

wave speed? I have v=ω/k=λ/T=λf I believe but what I don't know is whether or not that's what propagation speed is.

 

[BvU]

It is the good one in your case

 

[RavenBlackwolf]

It is the good one in your case

What do you mean by "the good one." I don't understand.

 

[RavenBlackwolf]

Oh I got it. The variable k is wavenumber, my professor never made that clear. So using:
ω=2π/T, T being the inverse of 39Hz or T=.0256
ω=245.04
v=ω/k=43m/s
so the answer is c.
This would've been a whole lot easier if that had been clear in my notes. Oops.

 

[Cutter Ketch]

Regarding your question about wavenumber, wavenumber is the number of waves that fit in a unit space. In other words it is 1/wavelength. Usually for convenience instead of how many waves per unit length it is defined as how many radians per unit length, that is

k = 2 π/λ

This is a convenience in that it simplifies a lot of equations and it is also proportional to energy.