7. A wave described by the function below propagates in a string under a tension of 0.18 N.?
the answers are in the box, but i dont understand the work needed to find them. help would be greatly appreciated.
- NCSLv 72 months ago
I agree with the other poster for the answer to (a).
But the PARTICLE'S velocity is given by
v(x,t) = dy/dt = 2.4x10^-3m * 270rad/s * cos(36x - 270t)
v(x,t) = 0.648m/s * cos(36x - 270t)
which is a maximum when cos() = 1 --
max v = 0.648 m/s ◄
7.5 m/s is the WAVE'S velocity.
Hope this helps!
- FiremanLv 72 months ago
Thus is a transverse harmonic wave traveling in the positive x-direction. Harmonic waves are sinusoidal waves. The displacement y of a particle in the medium is given as a function of x and t by
y(x,t) = Asin(kx - ωt)
Here k is the wave number, k = 2π/λ, and ω = 2πf is the angular frequency of the wave.
=>Thus v = ω/k
=>v = 270/36
=>v = 7.50 m/s
By v = √[T/µ]
=>v^2 = T/µ
=>µ = T/v^2 = 0.18/(7.50)^2 = 3.2 x 10^-3 kg/m OR 3.2 g/m