Question

A thin taut string is fixed at both ends and stretched along the horizontal x-axis with its left end at x =

0. It is vibrating in its third OVERTONE, and the equation for the vertical displacement of any point on

the string is y(x,t) = (1.22 cm) sin[(14.4 m-1)x] cos[(166 rad/s)t].

Answer 1

(a) What are the frequency and wavelength of the fundamental mode of this string? (b) How long is the string? (c) How fast do waves travel on this string?

y(x,t) = (1.22 cm) sin[(14.4 m-1)x] cos[(166 rad/s)t].

comparing with y(x,t) = A sin[kx] cos[wt].

A = 1.22 cm , k = 2pi/= 14.4 m^-1 , w =2pi*f = 166 rad/s

= 2pi/14.4 = 0.4363 m , f = 166/2pi = 26.42 hz

now as this belong to third overtone so ₄ = 0.4363 m , f₄ = 26.42 hz

(a) f =f₄ /4 = 6.6 hz ,    = 4₄ = 1.75 m

(b) L = /2 = 0.872 m

(c) v = f * = 6.6 * 1.75 = 11.5 m/s