Finding mass per unit length for stretched strng given tension?

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SUMMARY

The discussion focuses on calculating the mass per unit length of a stretched string under a tension of 5N, using the wave equation. Key parameters identified include an amplitude of 0.1 m, a wavelength of 0.4 m, and an angular frequency of 4 rad/s. The wave velocity is determined to be 0.1 m/s. The relationship between wave speed, tension, and density is established with the equation v = √(T/ρ), allowing for the calculation of mass per unit length.

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  • Understanding of wave equations and their parameters
  • Familiarity with tension in strings and its effects on wave propagation
  • Knowledge of angular frequency and wave velocity concepts
  • Basic principles of density and mass per unit length calculations
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  • Study the derivation of the wave equation for stretched strings
  • Learn about the relationship between tension, wave speed, and mass density
  • Explore graphical representations of wave functions
  • Investigate the effects of varying tension on wave properties
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Physics students, educators, and anyone interested in wave mechanics and the properties of stretched strings.

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[SOLVED] Finding mass per unit length for stretched strng given tension?

A transverse wave on a stretched string under Tension = 5N is defined by the equation:

y(x,t) = 0.1cos(2pi/5(x - 10t)

Find:

a) amplitude = 0.1 m

b) wavelength = 0.4 m

c) angular frequency = 4 rad/s

d) wave velocity = 0.1. m/s

e) mass per unit length ?

f) for t = 0, sketch how y varies with x. ?


I can do the first 4 parts be using the solution to the wave equation. Any ideas on how to do the other two bits? thanks.
 
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Hey thanks for anyone for looking at this. However I have been able to solve it another way. If anyone is interested the answer is:

wave speed v relates tension and density:

v = root(T/rho)

and you can set t=0 in that equation and you have something like y=acos(kx)
 

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