A wave travelling along a string is described by, y(x,t) = 0.005 sin ( 80.0x - 3.0 x). In which the numerical constants are in SI units ( 0.005m, 80.0 rad `m^(-1)` , and 3.0 rad `s^(-1)`) . Calculate (a) the amplitude , ( b) the wavelength , and (c ) the period and frequency of the wave. Also,calculate the displacement of the wave. Also, calaculate the displacement y of the wave at a distance x = 30.0 cm and time t =20s ?

Explanation

On comparing this displacement equation
`y(x,t)= a sin (kx-omega t+phi)` we find
(a) the amplitude of the wave is 0.005 m = 5 mm
(b) the angular wave number k and angular frequency `omega are k=80.0 m^(-1)and omega=3.0 s^(-1)`
We then relate the wavelength a to k through the equation
`T=2pi// omega=(2pi)/(3.0 s^(-1))=2.09s `
and frequency .`v=1//T=0.48Hz`
This displacement y at x=30.0 cm and time t-20s is given by
`y=(0.005m) sin (80.0xx0.3-3.0xx20)`
`=(0.005m)sin(-36+12pi)`
`=(0.005m) sin(97^(@))-=5mm`