Question

A string 3.30 m long and fixed at both ends is vibrating in its third harmonic. The maximum displacement of any point on the string is 4.00 mm. The speed of transverse waves on this string is 59.5 m/s.

(a) What are the wavelength and frequency of this standing wave?

wavelength	m
frequency	Hz

(b) Write the wave function for this standing wave.

Answer 1

The linear density of the rod is lambda = Q/L Consider a small element of the rod of length dr. The charge of the small element is dq = lambda dr The electric field due to this small element at a distance r is: dE = kdq/r^2 = k lambda dr/r^2 The net electric field at point due to rod is, E = integral^r + L/2_r - L/2 dE E = integral^r + L/2_r - L/2 k lambda dr/r^2 E = k lambda integral^r + L/2_r - L/2 dr/r^2 E = k lambda [- 1/r]^r + L/2_r - L/2 E = k(Q/L) [1/r - L/2 - 1/r + L/2] E = k(Q/L) [(r + L/2) - (r - L/2)/(r + L/2)(r - L/2)] E = k(Q/L) [L/(r + L/2)(r - L/2)] E = k(Q/L)[L/(r + L/2) (r - L/2)] E = kQ/(r + L/2) (r - L/2) E = Q/4 pi epsilon_0 (r^2 - L^2/4)