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### Course: Class 11 Physics (India)>Unit 19

Lesson 2: Wave characteristics

# The equation of a wave

In this video David shows how to determine the equation of a wave, how that equation works, and what the equation represents. Created by David SantoPietro.

## Want to join the conversation?

• why is pi in the wave equation?? not quite understanding why. thanks!
• @Hannah C.
The heart of the wave equations as David described them are trigonometry functions, sine and cosine. Trig functions take angles as arguments. The most natural units to express angles in are radians. The circumference of a circle = π times its diameter. The diameter is 2 times the radius, so C = 2πR. Now when the radius equals 1, C = 2π. The meaning of this is that any angle can be expressed in radians as an arclength on a circle of radius 1. 2π radians = 360 degrees. So the 2π in the cosine (or sine) function of a wave equation is a proportionality constant to turn a distance in meters for example into angle that can be input to the trig function so the trig function will output a height (distance).
• Why do we subtract (2pi x time/ time period) when the wave is moving right ? and add when moving to the left??
• If y(x)=cos(x-1) then at x=1 y=cos(0) so at x=1 you are seeing what would normally be at x=0 and in order to do that you have to move the point from the x=0 position to the x=1 position, which is moving the point or wave to the right. I hope I didn't confuse you more.
• what is the wave equation for longitudinal wave?
• The basic idea is the same, the only difference being that the particles now don't oscillate along the y-axis as in transverse waves, they now do so in the x-axis itself. So, instead of y(x,t) we use x(x,t). But that equation is very confusing since you can't know which is the input x and which is the output. So, it's convenient to replace one of them by a different variable.
So, the general equation of a longitudinal wave is:-
s(x,t)=Asin(kx-wx)
(1 vote)
• Will increasing frequency increase wave speed?
• Hello Xue,

Nope.

The speed at which the wave moves through a medium is constant. Actually, that is an oversimplification, the wave's velocity depends on the medium through which it is moving:

* Radio waves and light move at the speed of light...

* sound is a wave traveling through the air. The actual speed depends on temperature, humidity, and altitude...

* waves on the ocean are dependent on the depth of the ocean floor...

Regards,

APD
• How is he able to input any value for (x,t), in this case 5.2s and 3m with the wave having a constant velocity of 0.5m/s? Is this a mistake/bad example or am I missing something?
• It's not a mistake. The speed of the wave will not change depending on the values inputted into the wave function. Essentially, the only purpose of the function is to find out where the wave height will be at a certain time and distance.
• Why was there T (period) and t (time) in the original generalized equation, and in the example the t (time) was not considered ? Just the T (period) was considered.
• The goal was to find an equation of the given wave in terms of distance "x" and time "t," so that if you insert any distance and time, the equation will tell you the corresponding height.
• hi, at 8.22, why does the wave move towards left when we add a phase constant
• You could look at the phase constant as if it added to the wave's shift towards the next peak according to our chosen default point of time.
Such wave basically starts already further from its normal state at the time we start observing it.
• Can you use sin instead of course without changing the equation
• Hi there, I am confused about the phase factor (phi). What is it and how do we calculate it?

Thank you :)