A wave on a string is described by Dxt24cm sin2x84mt014s1 wh

A wave on a string is described by
D(x,t)=(2.4cm)× sin[2(x/(8.4m)+t/(0.14s)+1)], where x is in m and t is in s.

What is the wave speed?

What is the frequency?

What is the wave number?

At t=0.21s, what is the displacement of the string at x=9.1m?

Express your answer to two significant figures and include the appropriate units.

Solution

wave on a string A = Ao (sin(kx+wt))

compare the given equation with above form

here wave number k = 2/ L : L is the wavelenght = 8.4 m ; and angular frequency w = 2 /T ; T is the time period of the wave = 0.14sec

wave speed = w / k = 8.4 m / 0.14 sec = 60 m /sec

fequency = 1/T = 1/0.14 sec = 7.142

wave number k = 2/ L = 2/ 8.4m

plug the value fo x and t in D(x,t)=(2.4cm)× sin[2(x/(8.4m)+t/(0.14s)+1)],

                                                D(9.1, 0.21) = (2.4cm)× sin[2(9.1m/(8.4m)+0.21s/(0.14s)+1)],

                                                                      =1.673 m