# Transverse Wave on a String

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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 xmcos(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.

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davenn
Gold Member
2019 Award
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 thoughts

Dave

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

BvU
Homework Helper
2019 Award
In particular: do you have an expression for the speed of a wave on a string ?

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
Homework Helper
2019 Award
It is the good one in your case It is the good one in your case What do you mean by "the good one." I don't understand.

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
This would've been a whole lot easier if that had been clear in my notes. Oops.

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.

• BvU