A periodic wave can be written as:
[tex]y(x,t)=A sin (kx-\omega t)[/tex]
where
A is the amplitude, k is the wave number, x is the position, [tex]\omega[/tex] is the angular frequency and t is the time.
1. A represents the amplitude
Explanation: the term A inside the wave equation represents the amplitude, which is the maximum displacement of the wave (along the y-axis) with respect to tis equilibrium position. Basically, when the sine part of the wave is equal to 1, y=A, and the wave has the maximum displacement.
2. Wavelength
Explanation: the wavelength of a wave is defined as the distance between two successive crests (or between succesive throughs) of the wave.
The wavelength (indicated with [tex]\lambda[/tex]) is related to the wave number, k, by the equation
[tex]k=\frac{2\pi}{\lambda}[/tex]
3. [tex]\omega = 2 \pi f[/tex]
The frequency at which the source of the wave is oscillating, f, is related to the angular frequency [tex]\omega[/tex] by the relationship
[tex]\omega = 2 \pi f[/tex]
basically, f expresses the frequency in units of Hertz (1/s), while the angular frequency expresses the frequency in units of radians per second.
4. [tex]v=f \lambda[/tex]
The relationship between wave speed, wave frequency and wavelength is
[tex]v=f \lambda[/tex]
where
v is the wave speed
f is the frequency
[tex]\lambda[/tex] is the wavelength
We can observed that if the speed of the wave is constant, then the frequency and the wavelength are inversely proportional to each other.
