\n We are all familiar with waves. Sea waves, ripples of wave when\r\n a stone is thrown into water etc. are some of the everyday examples\r\n of waves that we see everyday. Now we will look at the mathematical description\r\n of waves.\r\n
\r\n\n Mathematically, a function \\(y=f(x,t)\\) is called a wave function if it\r\n satisfies the following differential equation:\r\n $$\\frac{\\partial^2 y}{\\partial x^2}=\\frac{1}{c^2}\\frac{\\partial^2y}{\\partial t^2}$$\r\n As you would've realized there are many functions which satisfy\r\n the above differential equation. The simplest of these is the sinusoidal wave function.\r\n The general form of the sinusoidal wave function is:\r\n $$y=A \\sin(\\omega t+kx+\\phi)$$\r\n Here, \\(\\omega\\) is called the \"angular frequency\" and \\(k\\) is called the \"wave number\".\n
\r\n\r\nAmplitude is the maximum value of the wave function. It is usually represented by \\(A\\).
\r\n\n The number of oscillations per second is called the frequency of a wave.\r\n The frequency is related to the angular frequency as follows:\r\n $$\\omega=2\\pi \\nu$$\r\n
\r\n\n The distance between two consecutive troughs or crests is called the wavelength.\r\n It is related to the wave number as follows:\r\n $$k=\\frac{2\\pi}{\\lambda}$$\n
\r\n\n The following diagram from Wikipedia shows\r\n the wavelength\n
\r\n\n The time taken by a wave to generate one wavelength is called the time period.\r\n The time period of a sinusoidal wave is:\r\n $$T=\\frac{2\\pi}{\\omega}$$\r\n
\r\n![Wikipedia](\"https://upload.wikimedia.org/wikipedia/commons/thumb/6/62/Sine_wavelength.svg/1200px-Sine_wavelength.svg.png\"){kind=link}