The equation of the wave is given by y=10^-4sin(100t-x÷10)m, find the velocity of the wave?
The equation of a wave is given by:
y = A sin(kx - ωt)
where A is the amplitude, k is the wave number, ω is the angular frequency, and t and x are time and position variables, respectively.
Comparing this equation with y = 10^-4 sin(100t - x/10) given in the question, we find that:
A = 10^-4
k = 1/10
ω = 100
The velocity of a wave is given by:
v = ω/k
Substituting the values, we get:
v = 100/(1/10) = 1000 m/s
Therefore, the velocity of the wave is 1000 m/s.
To find the velocity of the wave, we need to determine the coefficient of the x term in the equation.
The general equation for a wave is given by y = Asin(kx - wt), where:
- A is the amplitude of the wave,
- k is the wave number (2π/λ, where λ is the wavelength of the wave),
- w is the angular frequency (2πf, where f is the frequency of the wave),
- x is the position of the point on the wave, and
- t is the time.
Comparing this with the given equation, y = 10^(-4)sin(100t - x/10) m, we can see that:
- Amplitude (A) is 10^(-4).
- Wave number (k) is 1 (since k = 2π/λ and we don't have information about the wavelength).
- Angular frequency (w) is 100 (since w = 2πf and we don't have information about the frequency).
There is no coefficient of x in the given equation, which means the wave is not moving in the x-direction and that the velocity of the wave is zero.