Transverse waves on a string have wave speed 8.00 m/s, amplitude 0.0600 m, and w

Question

Transverse waves on a string have wave speed 8.00 m/s, amplitude 0.0600 m, and wavelength 0.285 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)
(i)
v = f
f = v/
f = 8.0 / 0.285
f = 28.1 hz

(ii)
T = 1/f
T = 1/28.1
T = 0.0355 s

(iii)
k = /c
k = 2*3.14*28.1 /8
k = 22.05 rad/m

(b)
y(x, t) = ym*sin(kx +/- t + )
y(x, t) = 0.060 *sin(22.05x +/- 176.5t + )

At y(0,0) = 0.060 *sin(22.05*0 +/- 176.5*0 + )
0.06 = 0.06 * sin()
= 90

y(x, t) = 0.060 *sin(22.05x +/- 176.5t + 90)
y(x, t) = 0.060 *cos(22.05x +/- 176.5t)

(c)
At x = 0.360
t = 0.150

y(x, t) = 0.060 *cos(22.05*0.360 +/- 176.5*0.150)
y(x, t) = 0.060 *cos(22.05*0.360 - 176.5*0.150)
y(x, t) = 0.057 m

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