Question

Simple harmonic wave, with phase velocity of 141ms^-1, propagates in the positive x-direction along a taut string that has a linear mass density of 5gm^-1. The maximum amplitude of the wave is 5cm and the wavelength is 75cm.

a) determine the frequency of the wave

b) write the wave function down the amplitude at time t = 0 and x = 0 is 2.5 cm.

c) calculate the maximum magnitude of the transverse velocity (of a particle on the string).

d) A second cord with linear mass density of 20gm^-1 is attached to the end. Calculate the amplitude and wavelength of the transmitted and reflected waves at this interface.

Answer 1

As given:

v = 141 m/s

mass density \mu = 5 g/m = 0.005 kg/m

amplitude A = 5 cm = 0.05 m

Wavelength \lambda = 75 cm = 0.75 m

(a) As the relation between speed and wavelength is:

frequency is,

hence,

(b) Wavefunction is given as:

hence, for x = 0 and t = 0

and for x = 2.5 cm = 0.025 m, t = 0

(c) As particle speed is:

speed is max, when cos is max, which is 1. hence, for cos(function) = 1,

(d) as amplitude of reflected and transmitted wave are given by:

and

As A_i = 0.05

density of first and second is 0.005 kg/m and 0.02 kg/m.

Tension in the string is given by

henc, we get

wavelengths can be found by v = \nu \lambda