Question

Oscillation of a 230 Hz tuning fork sets up standing waves in a string clamped at both ends. The wave speed for the string is 750 m/s. The standing wave has four loops and an amplitude of 1.6 mm. (a) What is the length of the string? (b) Write an equation for the displacement of the string as a function of position and time. Round numeric coefficients to three significant digits.

Answer 1

Here .

for the standing wave

wavelength = speed/frequecny

wavelength = 750/230

wavelength = 3.26 m

as there are 4 loops

length of string = 2 * wavelength

length of string = 2 * 3.26

length of string = 6.52 m

b)

NOw, for the wave ,

k = 2pi/wavelength

k = 2pi/3.26 = 1.93 rad/m

w = 2pi * f = 2pi * 230

w = 1440rad/s

A = 1.6 mm

NOw, for the equation of wave

y = A * sin(kx) * cos(wt)

y = 1.6 * sin(1.93x) * cos(1440t) mm

the equation of string displacement is 1.6 * sin(1.93x) * cos(1440t) mm