Longitudinal and Transverse waves transmitting at same Veloc

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SUMMARY

The discussion focuses on equating the speeds of longitudinal and transverse waves to solve for mass in a physics problem. The user successfully derived the transverse wave speed formula as V = SQRT(4T/(p*pi*d^2)), where T represents tension and p denotes density. The next step involves finding the speed formula for longitudinal waves in solids, which is essential for equating the two velocities. A suggested resource for this is provided, which outlines the mechanics of wave propagation.

PREREQUISITES
  • Understanding of wave mechanics, specifically longitudinal and transverse waves.
  • Familiarity with the formulas for wave speed, including V = SQRT(tension/u) for transverse waves.
  • Knowledge of mass density (rho) and its role in wave equations.
  • Basic algebra skills for manipulating equations and solving for variables.
NEXT STEPS
  • Research the speed of longitudinal waves in solids and its derivation.
  • Explore the relationship between tension, mass density, and wave speed in different mediums.
  • Study the principles of wave propagation and their applications in physics.
  • Review resources on mechanical waves, such as the provided link to the University of Denver's wave mechanics page.
USEFUL FOR

Students studying physics, particularly those focusing on wave mechanics, as well as educators seeking to enhance their understanding of wave equations and their applications in solving real-world problems.

Buster R
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Homework Statement


A picture of the problem can be found here: https://gyazo.com/a92447dcfebed53d4cbd12fc94300d9c[/B]

Homework Equations


So, I've already finished part A. For part B, I'm trying to figure out how to equate the two with mass on either side of the equation so that I can solve for it.

The Attempt at a Solution


Transverse wave speed = SQRT(tension/u), substitute (p*pi*d2 / 4)for mu since I don't have it -> V = SQRT(4T/p*pi*d2) where T is tension and p is rho.


Now I need to find a formula for speed of longitudinal wave that includes mass so that I can equate the two velocity formulas and solve for mass.

Any advice is much appreciated!
[/B]
 
Physics news on Phys.org
All you need to do is get the equation for the speed of a longitudinal wave in solids. I think this http://mysite.du.edu/~jcalvert/waves/mechwave.htm may help :).
 

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