Answer to Question #288772 in Physics for NICKO

Question #288772

Transverse waves on a string have a wave speed 8.00 m/s, amplitude 0.0700 m, and


wavelength 0.320 m. The waves travel in the -x-direction, and at t = 0, x = 0, the end of


the string has its maximum upward displacement. (a) Find the frequency, period, and


wave number of these waves. (b) Write a wave function describing the wave. (c) Find


the transverse displacement of a particle at x = 0.360 m at time t = 0.150 s

1
Expert's answer
2022-01-21T17:06:33-0500

Given:

v=8.00m/sv=8.00\:\rm m/s

A=0.0700mA=\rm 0.0700\: m

λ=0.320m\lambda=0.320\: \rm m


(a) the frequency

f=vλ=8.000.320=25.0Hzf=\frac{v}{\lambda}=\frac{8.00}{0.320}=25.0\:\rm Hz

the period

T=1f=125.0=0.0400sT=\frac{1}{f}=\frac{1}{25.0}=0.0400\:\rm s

the wave number

k=2πλ=6.280.320=19.6m1k=\frac{2\pi}{\lambda}=\frac{6.28}{0.320}=19.6\:\rm m^{-1}

(b) the wave function describing the wave

y(x,t)=Acos(2πftkx)y(x,t)=0.0700cos(157t19.6x)y(x,t)=A\cos(2\pi ft-kx)\\ y(x,t)=0.0700\cos (157t-19.6x)

(c)


y=0.0700cos(1570.15019.60.360)=0.0495my=0.0700\cos (157*0.150-19.6*0.360)\\ =-0.0495\:\rm m


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