Question

A wave travlling along a string described by. Y = 0.005 sin(80x -3t) in which the numerical const are in si units. Calculate a. Amplitude, b the wavelength, c the time period and frequency of the wave

Answer 1

The equation of a plane progressive wave is given as,

 

Y = A sin (ωt - kx)                                 ............(1)

 

Given:

Y=10 sin 2π(t - 0.005x)                            

Y=10 sin (2πt - 0.005 x 2πx)                      ............(2)

 

Comparing eq (1) and (2),

 

Amplitude A  = 10 m

 

ω = 2π rad s-1

 

k = 2π x 0.005 = 0.01π m-1

 

λ = 2π/k

  = 2π/(2π x 0.005)

  = 1/0.005

  = 200 m

 

Frequency = ω/2π             ( T = 2π/ω  → frequency = 1/T = ω/2π)

               = 2π/2π

               = 1 Hz

Answer 2

Answer:

amplitude= 0.005

k = 80

Ohmega = 3