In the given wave equation, y = 79 sin(2000t + 0.01x), we can extract the information about the amplitude, frequency, wavelength, and velocity of the wave. Let's break it down:
Amplitude (A): The amplitude of a wave represents the maximum displacement or height of the wave from its equilibrium position. In this case, the amplitude is 79.
Frequency (f): The frequency of a wave refers to the number of complete cycles or oscillations it undergoes per unit of time. In the given equation, the coefficient of 't' is 2000, which corresponds to the angular frequency (ω = 2πf). Therefore, the angular frequency is 2000 radians per second. To find the frequency (f), we divide the angular frequency by 2π:
ω = 2πf 2000 = 2πf f = 2000 / 2π ≈ 318.31 Hz
So, the frequency of the wave is approximately 318.31 Hz.
Wavelength (λ): The wavelength of a wave represents the spatial extent of one complete cycle of the wave. In the given equation, the coefficient of 'x' is 0.01. Since the general equation for a sinusoidal wave is y = A sin(kx - ωt), where k is the wave number (k = 2π/λ), we can determine the wavelength (λ) by calculating the reciprocal of the wave number:
k = 2π/λ 0.01 = 2π/λ λ = 2π / 0.01 = 200π
Therefore, the wavelength of the wave is 200π.
Velocity (v): The velocity of a wave represents the speed at which the wave propagates through a medium. For a sinusoidal wave, the velocity is given by the product of the frequency and wavelength:
v = fλ v = (318.31 Hz) * (200π) v ≈ 200π * 318.31 v ≈ 200 * 3.14159 * 318.31 ≈ 200 * 1000 ≈ 200,000 m/s
Thus, the velocity of the wave is approximately 200,000 m/s.
To summarize:
- Amplitude (A) = 79
- Frequency (f) ≈ 318.31 Hz
- Wavelength (λ) = 200π
- Velocity (v) ≈ 200,000 m/s