Question

A transverse wave on a cable is described by the function y(x,t)=2.3cos(4.7x+12t−π/2), where distance is measured in meters and time in seconds. If the tension in the cable is 25 N, what is the linear mass density of the cable?

Answer 1

here,

y(x,t) = 2.3 * cos(4.7 x + 12 t - pi/2)

on compairing the given equation with y(x,t) = A * cos(K * x + w * t - pi/2)

K = 4.7 m^-1 , w = 12 rad/s

the wavelength , lamda = 2*pi /K

lamda = 2*pi /4.7 m = 1.34 m

the frequency , f = w /2pi

f = 12 /(2pi) Hz = 1.91 Hz

let the linear mass density be u

the tension in the string , T = 25 N

the speed of wave , v = f * lamda = sqrt(T /u)

1.91 * 1.34 = sqrt(25 /u)

u = 3.81 kg/m

the linear mass density of cavle is 3.81 kg/m