In the stationary wave described by $y(x,t) = 0.06 \sin(2\pi x/3) \cos(120\pi t)$ for a 1.5 m long s

Question

In the stationary wave described by $y(x,t) = 0.06 \sin(2\pi x/3) \cos(120\pi t)$ for a 1.5 m long string of mass $3.0 	imes 10^{-2}$ kg, what is the tension in the string?

Professor PC Thomas Classes · Answer

Frequency $f = \omega / 2\pi = 120\pi / 2\pi = 60$ Hz. Wavelength $\lambda = 3$ m. Speed $v = f\lambda = 180$ m/s. Linear mass density $\mu = 0.03 / 1.5 = 0.02$ kg/m. Tension $T = \mu v^2 = 0.02 	imes (180)^2 = 648$ N.