Question

A sinusoidal wave describe by y (x, t)=3.0sin (3.52t-2.01x ) cm. Where x is along wave propagation. Determine the amplitude, wave number, wavelength, frequency &velocity of the wave.

Answer 1

velocity = f× wave length
= 0.72×3.12 = 1.62

Answer 2

here given equation
y = 0.3sin(3.52t -2.01x)
but we standard equation of wave is
y = Asin(wt ± kx)
where A is amplitude , w is angular frequency, k is wave number .

compare both of these ,

A = 0.3 cm
w = 3.52 cycle /sec
k = 2.01 cycle/m

we know,

w = 2π× frequency,
3.52 = 2π × frequency
frequency = 3.52/2π Hz

also K =2π/wavelength

2.01 = 2π /wavelength

wavelength= 2π/2.01

wave no = k = 2.01

velocity of wave = wavelength x frequency = 2π/2.01 x 3.52/2π = 3.52/2.01 m/s