Pretend a system is having Transverse waves. And those transverse waves on a str

Question

Pretend a system is having Transverse waves. And those transverse waves on a string have wave speed 8.00 m/s amplitude 0.0700m and wavelength 0.320m. The waves travel in the -x dierection, and at t=0 the x=0 end of the string has its maximum upward displacement

a) Find the frequency, period, aand wave number of these waves.

b) Write a wave function describing the wave

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

d) How much time must elapse from the instant in part c) until the particle at x=0.360m next has maximum upward displacement?

Explanation / Answer

a) F=v/lambda = 8/0.32 = 25 HZ

T=1/F = 0.04sec

wave number = 2*pi/lambda = 19.635

b) equation y(x,t) = 0.07sin(2*pi*F*t +kx) = 0.07sin(157.0796 t + 19.635x)

c) y(0.36,0.15) = 0.07sin(157.0796 *0.15 + 19.635*0.36) = -0.0495m

d) 0.07 = 0.07sin(157.0796 *t + 19.635*0.36)

and solving for t,we get

t=0.1550sec at 10pi

hence time elapse = 0.155-0.150 = 0.005sec

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