Question #326228

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


1
Expert's answer
2022-04-11T12:08:30-0400

(a) Write a wave function describing the wave

y(x,t)=Acos(2πft+2πλx)y(x,t)=A\cos(2\pi ft+\frac{2\pi}{\lambda}x)

f=v/λ=8.0/0.400=20Hzf=v/\lambda=8.0/0.400=20\:\rm Hz

y(x,t)=0.0600mcos(40πt+5πx)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=0.0600mcos(40π0.150+5π0.350)=0.0424my=0.0600{\:\rm m}\cos(40\pi *0.150+5\pi *0.350)\\ =0.0424\:\rm m


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