Transverse waves on a string have wave speed 8.00 m/s, amplitude 0.0750 m, and w

Question

Transverse waves on a string have wave speed 8.00 m/s, amplitude 0.0750 m, and wavelength 0.300 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

wave speed v = 8 m/s

amplitude A = 0.075 m

wavelength = 0.3 m

(a)

frequency f = speed/wavelength = 8/0.3 = 26.7 Hz

time period T = 1/f = 0.0375 s

wavenumber = k = 2pi/wavelength = 2*pi/0.3 = 20.9 rad/m

(b)

wave function y = A*cos(wt + kx)

w = 2*pi*f = 2*pi*26.7 = 167.7 rad/s

y = 0.075*cos(167.7t + 20.9x)

(c)

y = 0.075*cos((167.7*0.15)-(20.9*0.36)) = 0.0258 m = 2.58 cm

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.