The equation of a transverse wave is
Y(x, t) = 0.02 cos(10$\pi$x - 400$\pi$t)
Where the units are SI. The velocity of the wave is
A) 0.20$\pi$ m/s
B) 8$\pi$ m/s
C) 40 m/s
D) 0.20 km/s
E) 0.40$\pi$ km/s

Question

Quizplus · Accepted Answer

The velocity of the wave can be found using the equation:
v = λf
where λ is the wavelength and f is the frequency. 
In the given equation, the wavelength is given by:
λ = 2π/k 
where k is the wave number, which is equal to 10π/λ. 
Substituting the given values, we get:
λ = 2π/(10π/λ) 
λ^2 = 20 
λ = √20 
λ = 2√5 m
The frequency is given by:
f = ω/(2π) 
where ω is the angular frequency, which is equal to 400π. 
Substituting the given values, we get:
f = 400/2 = 200 Hz
Substituting the values of λ and f in the equation for velocity, we get:
v = λf = (2√5)(200) = 400 m/s
Therefore, the correct choice is C, 40 m/s.

The Equation of a Transverse Wave Is Y(x, T) = π\piπ

The Equation of a Transverse Wave Is
Y(x, T) = $\pi$