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
when does 200 pi t = 2 pi ??? (when t = T :)
T = 2/200
T = 0.01 second
when does pi x/17 = 2 pi ? (when x = L)
L = 34 meters
frequency = 1/T = 100
for velocity, constant phase = constant argument
200 t = x/17
x/t = 17*200
To find the answers, let's break down the given wave equation:
y = a sin(200πt - (πx/17))
1) The Wavelength:
The wavelength (λ) of a wave is the distance between two consecutive points on the wave that are in phase. In the wave equation y = a sin(kx - ωt), k represents the wave number, which is equal to 2π divided by the wavelength. So, in our given wave equation, we can see that k = 200π and rearrange it to find the wavelength:
k = 2π / λ
Therefore, the wavelength (λ) is given by:
λ = 2π / k
= 2π / (200π)
= 1 / 100
= 0.01 units
So, the wavelength of the wave is 0.01 units.
2) The Velocity:
The velocity (v) of a wave is the rate at which a point on the wave moves in a given direction. It can be calculated using the formula:
v = λ * f
where λ is the wavelength and f is the frequency of the wave. In our case, we've already determined the wavelength to be 0.01 units. To find the frequency, we need to determine the angular frequency (ω) first.
The angular frequency (ω) can be found from the equation:
ω = 2πf
Comparing it with our given wave equation, we can deduce that ω = 200π. Rearranging the formula for the angular frequency, we find:
f = ω / (2π)
= 200π / (2π)
= 100 Hz
Now, substituting the values of λ and f into the velocity formula, we get:
v = λ * f
= 0.01 * 100
= 1 unit per second
Therefore, the velocity of the wave is 1 unit per second.
3) The Frequency:
As determined above, the frequency (f) of the wave is 100 Hz.
4) The Period:
The period (T) of a wave is the time taken for a complete cycle of the wave to pass a given point. It is the reciprocal of the frequency, so:
T = 1 / f
= 1 / 100
= 0.01 seconds
Thus, the period of the wave is 0.01 seconds.