15.22 A travelling harmonic wave on a string is described by

y(x, t) = 7.5 sin (0.0050x +12t + $\mathit{\pi }$ /4)

(a) What are the displacement and velocity of oscillation of a point at x = 1 cm, and t = 1 s? Is this velocity equal to the velocity of wave propagation?

 

(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.

A set of 16 tuning forks are so arranged that each produce 4 beats with the previous one. If the frequency of last tuning fork is double that of first, the frequency of third tuning fork is

A pipe open at both ends produces a note of fundamental frequency V₁. When the pipe is kept with (1/3)^rd of its length in water, it produces a note of frequency V₂.The value of V₁/ V₂ is

A string of linear density 0.4 kg/m is stretched with force of 1000 N. A transverse wave is set up along it. The speed of the wave is

A particle is executing S.H.M. its potential energy v/s displacement graph is given by

The value of restoring force constant is :-

A heavy rope is suspended from rigid support. A wave pulse is set up at the lower end. Then