A sinusoidal transverse wave is travelling along a string in the negative direct

Question

A sinusoidal transverse wave is travelling along a string in the negative direction of an x axis. The figure shows a plot of the displacement as a function of position at time t = 0; the y intercept is 4.0cm. The string tension is 4.9N, and its linear density is 26 g/m. Find the (a) amplitude, (b) wavelength, (c) wave speed, and (d) period of the wave. (e) Find the maximum transverse speed of a particle in the string. If the wave is of the form y(x,t) = y_m sin (kx - omega t + phi), what are (f) k, (g) omega, and (h) phi, and (i) the correct choice of sign in front of omega?

Explanation / Answer

a) Clearly from the graph, A = 5 cm

b) y takes the values of 4 and -4 at x = 0 and x = 20 respectively. So, the half wavelength is 20 cm. So, the wavelength of the wave is 40 cm.

c) Wave speed, v = (T/)1/2 = [4.9 / (26 * 10-3)]1/2 = 13.7 m/s

d) T = 1/f = /v = 0.4 / 13.7 = 0.03 s

e) Maximum transverse speed, vp = A(2f) = 0.05 * 2 * (1/0.03) = 10.5 m/s

f) k = 2/ = 2/0.4 = 15.7 rad/m

g) = 2/T = 2/0.03 = 209.4 rad/s

h) At x = 0 and t = 0, y = 4 cm

=> 4 = 5sin

=> = sin-1(4/5) = 53o

i) Since wave is moving to the left, the correct choice of sign should be negative.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

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