The transverse displacement of a string clamped at both ends is given by $y(x,t) = 0.06 \sin(2\pi x/

Question

The transverse displacement of a string clamped at both ends is given by $y(x,t) = 0.06 \sin(2\pi x/3) \cos(120\pi t)$, where $x$ is in meters and $t$ in seconds. What is the wavelength of the constituent travelling waves?

Professor PC Thomas Classes · Answer

The spatial part of the stationary wave is $\sin(kx)$. Here, $k = 2\pi/3$. Since $k = 2\pi/\lambda$, we get $\lambda = 3.0$ m.