Transverse Wave on a String

In summary: For waves on a string, the wavenumber is 5.7m-1. Regarding your question about what equation to use, you can use the wave equation, xmcos(ωt+Φ), or the displacement equation, x(t+θ). The phase angle in either equation is represented by θ.
  • #1
< 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 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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  • #2
Hi there
welcome to PF :smile:

I have asked for this to be moved to homework section

RavenBlackwolf said:
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
 
  • #3
Oh I didn't know there was one, sorry.
 
  • #4
In particular: do you have an expression for the speed of a wave on a string ?
 
  • #5
BvU said:
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.
 
  • #6
It is the good one in your case :smile:
 
  • #7
BvU said:
It is the good one in your case :smile:
What do you mean by "the good one." I don't understand.
 
  • #8
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.
 
  • #9
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.
 
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What is a transverse wave on a string?

A transverse wave on a string is a type of wave that travels along a string or rope in a perpendicular direction to the string's length. This means that as the wave moves, the particles of the string move up and down or side to side, rather than back and forth.

What are the properties of a transverse wave on a string?

The properties of a transverse wave on a string include amplitude, wavelength, frequency, and speed. Amplitude is the maximum displacement of the string from its resting position. Wavelength is the distance between two consecutive peaks or troughs of the wave. Frequency is the number of complete waves passing a point in one second. And speed is the rate at which the wave travels through the string.

How is energy transferred in a transverse wave on a string?

In a transverse wave on a string, the energy is transferred through the oscillation of the particles of the string. As the wave moves, the particles of the string move up and down or side to side, transferring energy from one particle to the next. This allows the wave to travel along the string without the particles themselves moving along with it.

What factors affect the speed of a transverse wave on a string?

The speed of a transverse wave on a string is affected by the tension of the string, the density of the string, and the length of the string. An increase in tension or density will result in an increase in speed, while an increase in length will result in a decrease in speed. The relationship between these factors can be described by the equation v = √(T/μL), where v is the speed, T is the tension, μ is the density, and L is the length of the string.

How is a transverse wave on a string different from a longitudinal wave on a string?

A transverse wave on a string and a longitudinal wave on a string differ in the direction of the particle motion and the direction of energy transfer. In a transverse wave, the particles of the string move perpendicular to the direction of wave motion, while in a longitudinal wave, the particles move parallel to the direction of wave motion. Additionally, in a transverse wave, the energy is transferred through the oscillation of particles, while in a longitudinal wave, the energy is transferred through compression and rarefaction of the particles.

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