Q.15.22 A travelling harmonic wave on a string is described by

y(x,t)=7.5\: \sin (0.0050\: x+12t+\pi /4)

(b) Locate the points of the string which have the same transverse displacements and velocity as the x=1\: cm point at t=2\: s, 5 s and 11 s.

Answers (1)
S Sayak

The wavelength of the given wave is

\\\lambda =\frac{2\pi }{k}\\ \lambda =\frac{2\pi }{0.005 cm^{-1}}\\ \lambda =1256cm\\ \lambda =12.56m

The points with the same displacements and velocity at the same instant of time are separated by distances n\lambda.

The points of the string which have the same transverse displacements and velocity as the x=1\: cm point at t=2\: s, 5 s and 11 s would be at a distance of

\pm \lambda ,\pm 2\lambda ,\pm 3\lambda ... from x = 1cm.

\lambda =12.56m

Therefore all points at distances \pm 12.56m,\pm 25.12m,\pm 37.68m from the point x=1cm would have the same transverse displacements and velocity as the x=1\: cm point at t=2\: s, 5 s and 11 s.

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