Answer:
d. 0.5 m/s along -x direction
Explanation:
Wave: A wave is a disturbance, that travels through a medium and transfers energy from one point to another, without causing any permanent displacement of the medium itself.
The general equation of a traveling wave can be expressed as
y = Acos(2πft-2πx/λ).................................. Equation 1
Where A = amplitude of the wave, f = frequency of the wave, λ = wavelength of the wave, x = linear distance, t = time, π = pie.
From the question,
the equation of the moving wave is
y = 0.12cos(4x+2t) ................................... equation 2
Comparing equation 1 and 2
-2πx/λ = 4x
λ = -2π/4
λ = -2(3.14)/4
λ = -1.57 m.
Also,
2πft = 2t
f = 2t/2πft
f = 1/π
f = 1/3.14
f = 0.3185 Hz.
Recall that
v = λf.......................... Equation 3
Substitute the value of f and λ into equation 3
v = -1.57(0.3185)
v = - 0.5 m/s.
Note: v is negative because - x direction
Hence the right option is d. 0.5 m/s along -x direction
