Question

A wave is described by y = 0.019 8 sin(kx - ωt), where k = 2.06 rad/m, ω = 3.68 rad/s, x and y are in meters, and t is in seconds.

(a) Determine the amplitude of the wave.

m

(b) Determine the wavelength of the wave.

m

(c) Determine the frequency of the wave.
Hz

(d) Determine the speed of the wave.
m/s

Answer 1

The equation representing the given wave is

y = 0.019 8 sin(kx - ωt),

where, k = 2.06 rad/m and ω = 3.68 rad/s

the standard equation representing a wave is

y = A sin(kx - ωt), where A is the amplitude of the wave.

Comparing the two equations , we get A = 0.0198 m

(a)

The amplitude of the wave, A = 0.0198 m

(b)

Propagation constant, k = 2π/λ

Wavelength of the wave, λ = 2π/k = 2 x 3.14 /2.06 = 3.05 m

( c)

Angular frequency, ω = 2πf

Frequency of the wave, f = 2π/ω = 2 x 3.14/3.68 = 1.71 Hz

( d)

The speed of the wave, V = fλ = 1.71 x 3.05 = 5.21 m/s

answered by: anonymous