Show that the velocity of travelling wave produced in a string is `v= sqrt((T)/(mu))`

On what factors velocity of transverse wave in a string depends ?

The equation of a standing wave, produced on a string fixed at both ends, is y = (0.4 cm) sin[(0.314 cm^-1) x] cos[(600pis^-1)t] What could be the smallest length of the string ?

The equation of a wave travelling on a string is y = 4 sin {(pi)/(2) (8 t - (x)/(8)) } , where x , y are in cm and t in seconds . The velocity of the waves is ……….. .

Show that for a wave travelling on a string y_(max)/v_(max)=v_(max)/a_(max) wher the symbols have usual meanings. Can we use componendo and dividendo taught in algebra to write (y_(max)+v_(max))/(y_(max)-v_(max))=(v_(max)+a_(max))/(v_(max)-a_(max))?

A travelling harmonic wave on a string is described by y(x,t) = 7.5 sin (0.005 x + 12t+ pi//4) (a) what are the displacement and velocity of oscillation of a point at x=1 cm, and t=1s? 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=2s, 5s and 11s