show work plz A transverse wave, moving along the x-axis is described by the wav
ID: 2116838 • Letter: S
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show work plz
A transverse wave, moving along the x-axis is described by the wave equation: y(x, t) = 2 cos (3x + 4t) where lengthes are given in cm and time is in second. Read off the values of the period, the wavelength, and compute the velocity of this wave. In what direction is this wave moving? At the origin, the function y(0, t) is that of a harmonic oscillator. If the mass is 5 g, calculate the velocity and acceleration of that mass when the time is a quarter of a period. Calculate the energy and the spring constant for the simple harmonic motion described in part (b)Explanation / Answer
comparing it with the equation 1)y=acos(kx+wt) w=4=2*pi/T => T=2*pi/4= pi/2 and K=3 => 2*pi/wavelength=3 wavelength=2/3*pi now velocity=w/K=4/3 cm/s the wave is moving in the negative x direction. b) y(0,t)=2cos(4t) since m=5g at time t=T/4=pi/(2*4)=pi/8 y(0,T/4)=2cos(4*pi/8)=0 velocity=w*sqrt(a^2-y^2)=w*a=4*2=8cm/s and accleration=-w^2x=-w^2*0=0. c)spring constant K=m*w^2=5/1000*4^2=0.08 Energy=1/2K*a^2=1/2*0.008*2^2=0.016 J
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