Wave Velocity in Terms of Tension

In summary, the conversation discusses a homemade wave "machine" made with brass rods and tape, and how the wave velocity can be determined through changing the tension on the sides. The estimated wave velocity in practice is around 30-130cm/s, but may be affected by factors such as the length of the medium and the type of tape used. The conversation also mentions the possibility of changing the concentration of rods or distance between each rod to affect the wave velocity.
  • #1
bfr
52
0
A few friends and I built a wave "machine." It's made by laying out brass "rods" about a foot long next to each other about an inch or so apart on tape, and then taping the top side. When holding both sides of this "machine," when one strikes one rod at one end, it makes the rod in front of it move, which makes the rod in front of it move etc., creating a "wave."

For a wave like this, is there any way to determine the wave velocity in terms of a changing tension (which would be changed by pulling on either side of the wave "machine" more or less).
 
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  • #2
well

[tex]v=\sqrt{\frac{T}{\mu}[/tex]

where [itex]\mu[/itex] is the mass per unit length.
 
  • #3
bfr said:
A few friends and I built a wave "machine." It's made by laying out brass "rods" about a foot long next to each other about an inch or so apart on tape, and then taping the top side. When holding both sides of this "machine," when one strikes one rod at one end, it makes the rod in front of it move, which makes the rod in front of it move etc., creating a "wave."

Neat. Can you tell us a ballpark estimate of the wave velocity you get in practice? I've wanted to build something like this as I am a private tutor and would like to have a wave motion demo for students. With the spring I have used the waves just move too fast to watch.
 
  • #4
My friend calculated that the wave moved anywhere from about 30cm/s to to 130cm/s when we varied how hard we pulled on each side (he got these velocities by timing the waves). It looked kind of fast. The entire medium was relatively short (70cm maybe), though, which made it harder to time and made it look like it went by faster, and we used duct tape, which because of its width, probably also sped up (and dampened) the wave (we did this though because otherwise some rods would be lopsided with thinner tape).

rock.freak667: OK, thanks.

EDIT: Quick question - do you think changing the concentration of rods / distance between each rode would increase or decrease the wave velocity?
 
Last edited:

What is wave velocity in terms of tension?

Wave velocity in terms of tension refers to the speed at which a wave travels through a medium under a certain amount of tension. This is a measure of how quickly the wave energy is transferred from one point to another.

How does tension affect wave velocity?

Tension plays a crucial role in determining the velocity of a wave. As tension increases, the velocity of the wave increases as well. This is because higher tension results in a stiffer medium, allowing the wave to travel faster.

What is the relationship between tension and wavelength?

There is a direct relationship between tension and wavelength. As tension increases, the wavelength of the wave also increases. This is because higher tension results in a higher wave velocity, causing the wave to cover a longer distance in the same amount of time.

How is wave velocity in terms of tension calculated?

The formula for calculating wave velocity in terms of tension is v = √(T/μ), where v is the wave velocity, T is the tension in the medium, and μ is the linear mass density of the medium.

What are some real-life applications of wave velocity in terms of tension?

Wave velocity in terms of tension is an important concept in many fields, including engineering, acoustics, and music. It is used to understand and design structures that can withstand high tension, as well as to optimize sound quality in musical instruments based on the tension of their strings. It is also relevant in understanding the behavior of ocean waves and their effects on coastal structures.

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