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 wavelengt

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?

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niczorrrr 3 weeks 2021-08-31T12:36:43+00:00 1 Answers 0 views 0

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    2021-08-31T12:37:44+00:00

    Answer: a) 25 Hz, 0.04s, 19.64. b) y(x, 0) = 0.07 sin 19.64x. c) – 0.019 m. d) 0.045s

    Explanation: wave speed (v) = 8m/s, amplitude (A) = 0.07m and wavelength (λ) = 0.32m

    A)

    Recall that v = fλ

    8 = f( 0.32)

    f = 8/ 0.32 = 25 Hz.

    But T = 1/f

    T = 1/25 = 0.04s

    Wave number (k) = 2π/λ= 2(3.142)/0.32 = 19.64

    B)

    y(x, t) = A sin (kx – wt) but t =0

    Hence, y(x, 0) = A sin kx

    y(x, 0) = 0.07 sin 19.64x

    C) recall that y(x, t) = A sin (kx – wt), we are to find y(x,t) when x = 0.360m and t = 0.150s

    w=2πf = 2(3.142)× 25 = 157.14 rad/s

    A = 0.07m

    k = 19.64

    y(x,t) = 0.07 sin {19.65(0.360) – 157.14(0.15)}

    y(x,t) = 0.07 sin { 7.074 – 23.571}

    y(x,t) = 0.07 sin (-16.497)

    y(x,t) = 0.07 × (-0.283)

    y(x,t) = – 0.019 m

    D) wave speed = 8m/s, x = 0.360 m

    Wave speed = distance /time

    8 = 0.360/t

    t = 0.360/8 =0.045s

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