Answer to Question #327000 in Physics for Naruto

Question

The waves on a string have wave speed 8.00m/s, amplitude 0.0600m, and wavelength 0.400m. The waves travel in the -x direction and at t = 0s, the end of the string has its maximum upward displacement.

(a) Write a wave function describing the wave and

(b). Find the transverse displacement of a particle at x = 0.350m at time t = 0.150s

Answer 1

(a) Write a wave function describing the wave

$$y(x,t)=A\cos(2\pi ft+\frac{2\pi}{\lambda}x)$$ $$f=v/\lambda=8.0/0.400=20\:\rm Hz$$ $$y(x,t)=0.0600{\:\rm m}\cos(40\pi t+5\pi x)$$

(b) Find the transverse displacement of a particle at x = 0.350m at time t = 0.150s

$$y=0.0600{\:\rm m}\cos(40\pi *0.150+5\pi *0.350)\\ =0.0424\:\rm m$$