Question

A harmonic wave with a frequency of 90 Hz and an amplitude of 0.025 m travels along a string to the right with a speed of 20 m/s.
a)Write a suitable sine wave function for this wave in terms of x and t.
b) Find the maximum speed of a point on the string.
(c) Find the maximum acceleration of a point on the string.

Answer 1

y = .025 sin (2 pi f t - 2 pi x/L)
L = v T = v/f
so
y = .025 sin 2 pi f t - 2 pi x f/v)
= .025 sin 2 pi f( t - x/v)
= .025 sin 2 pi *90 (t - x/20)
= .025 sin 2 pi (90 t - 4.5 x)
-------------------------------------
dy/dt = speed = 180 pi *.025 cos 2 pi (90 t - 4.5 x)
d^2y/dt^2 = acceleration =- .025 (180 pi)^2 sin 2 pi (90 t - 4.5 x) = -(180 pi)^2 y