A progressive wave equation is represented by Y=A sin 2π (0.15t -0.1x)
Determine;
i. Frequency
ii. Period
III. Wave length
iv. Velocity of wave
To determine the frequency, period, wavelength, and velocity of the wave represented by the equation Y = A sin(2π(0.15t - 0.1x)), we can analyze the equation and use the formulas related to wave properties.
i. Frequency:
The frequency (f) of a wave is the number of cycles (or vibrations) per unit time. In the given equation, the coefficient of 't' represents the angular frequency (ω), which is 2π(0.15). The frequency can be determined by dividing the angular frequency by 2π:
f = ω / (2π)
Substituting the values:
f = 0.15 / (2π) ≈ 0.0238 Hz
ii. Period:
The period (T) of a wave is the time taken for one complete cycle. The period is the reciprocal of the frequency:
T = 1 / f
Substituting the frequency value obtained in the previous step:
T = 1 / 0.0238 ≈ 41.93 seconds
iii. Wavelength:
The wavelength (λ) is the distance between two successive points in a wave that are in phase. In the given equation, the coefficient of 'x' represents the angular wave number (k), which is 2π(-0.1). The wavelength is given by the formula:
λ = 2π / k
Substituting the values:
λ = 2π / (-0.1) ≈ -62.83
Note that the wavelength obtained is negative because the negative sign in the equation indicates a wave traveling in the negative x-direction.
iv. Velocity of wave:
The velocity (v) of a wave is the speed at which a wave propagates through a medium. It can be calculated by multiplying the frequency and wavelength:
v = f * λ
Substituting the values:
v = 0.0238 * -62.83 ≈ -1.50 m/s
Here, the velocity obtained is negative because the wave is traveling in the negative x-direction.