Finding mass per unit length for stretched strng given tension?

[coffeem]

[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.

 

[coffeem]

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)

 

[Moetasim]

Based on the given information, the mass per unit length of the stretched string can be calculated using the following formula:

μ = (T/υ^2) * λ

Where,

μ = mass per unit length

T = tension in the string

υ = wave velocity

λ = wavelength

Substituting the values from the given information, we get:

μ = (5N / (0.1 m/s)^2) * 0.4 m

μ = 200 kg/m

Therefore, the mass per unit length for the stretched string is 200 kg/m.

For t = 0, the equation becomes:

y(x,0) = 0.1cos(2pi/5x)

This represents a simple harmonic motion with an amplitude of 0.1 m and a wavelength of 0.4 m. The graph of this function would be a cosine wave with an amplitude of 0.1 and a period of 0.4 m. The wave would start at the origin and oscillate between positive and negative values with a period of 0.4 m.