A progressive wave equation is given by
y=a sin (200(pie)t -(pie)x/17)
and???
This is the full question
A progressive wave equation is given by
y=a sin (200(pie)t -(pie)x/17)
Find;
1) The wavelength
2) Velocity
3) Frequency
4) Period
To find the wave speed of the progressive wave described by the equation y = a sin (200πt - (πx/17)), we can use the general form of a wave equation:
y = A sin (kx - ωt + ϕ)
where:
- y represents the displacement of the wave at a particular point x and time t,
- A is the amplitude of the wave,
- k is the wave number (2π/λ, where λ represents the wavelength),
- ω is the angular frequency (2πf, where f is the frequency), and
- ϕ is the phase constant.
In our given equation, comparing it with the general form, we can see that:
- A = a (given)
- k = π/17
- ω = 200π
To find the wave speed, we can use the formula:
v = ω/k
Substituting the given values:
v = (200π) / (π/17)
v = 200π * (17/π)
v = 3400 m/s
Therefore, the wave speed of the progressive wave described by the given equation is 3400 m/s.