Transverse waves on a string have wave speed 8.00 m/s, amplitude 0.0650 m, and w

Question

Transverse waves on a string have wave speed 8.00 m/s, amplitude 0.0650 m, and wavelength 0.315 m. The waves travel in the -x-direction, and at t = 0 the x = 0 end of the string has its maximum upward displacement. (a) Find the following properties of these waves.
frequency
f = Hz
period
T = s
wave number
k = rad/m

(b) Write a wave function describing the wave. (Use the following as necessary: t and x.)
y(x, t) = m


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

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

Explanation / Answer

a)

f=V/lambda =8/0.315=25.4 Hz

Period

T=1/f =1/25.4 =0.03938 s

Wave number

K=2pi/lambda=2pi/0.315=19.95 rad/m

b)

Y(x,t)=ACos(Kx+Wt)

c)

W=2pi*f=2pi*25.4=159.6 rad/s

Y(x,t)=0.065Cos(19.95x+159.6t)

at (0.36,0.15)

Y(0.36,0.15)=0.065Cos(19.95*0.36+159.6*0.15)

Y(0.36,0.15)=0.0622 m

d)

19.95*0.36+159.6*0.15/2pi =4.95322

t=2pi(5-4.95322)/159.6

t=0.00184 s or 1.84 ms

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