Four traveling waves are described by the following equation

Four traveling waves are described by the following equation, where all quantities are measured in (text not clear) Which pair of these waves have the same period Which pair is travelling to the left What is the wavelength of wave II What is the propagation speed of wave III A 2.0 string is fixed at both ends and tightened to a tension of 104 N, until the wave speed is 78 m/s. What is the frequency of the standing wave What is the total mass of the string Write an equation for the shape of the string y(x, t)

Solution

1) a) I & III and II & IV because these pairs have same angular frequency(w) . T = 2pi/w

b) Pair II and III will travell to the left as speed is negative for both.

c) From II, 2pi/wavelength = 6

wavelength = 1.047 m

d) From wave III, k = 6, w = -21

Propagation speed = w/k = -21/6 = -3.5 m/s

2) From figure wavelength = L/3 = 2/3 = 0.67 m

a) frequency = f =v/lambda = 78/0.67 = 116.42 Hz

b) As v^2 = T/(m/L) ====> m = T*L/v^2

m = 104*2/78^2 = 0.034 kg = 34g