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Standing waves

by nil1996
Tags: standing, waves
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nil1996
#1
Oct17-13, 01:33 AM
P: 296
Equation of standing waves→ y=Asinkxcosωt

What do i get if i differentiate the above equation with respect to "x" ?
Do i get the rate of change of amplitude when i put t=0?
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NihalSh
#2
Oct17-13, 01:52 AM
P: 199
when you differentiate it with respect to x, then you get slope of the curve/wave at a given instant ##\frac{dy}{dx}=slope##.
NihalSh
#3
Oct17-13, 01:54 AM
P: 199
rate of change of amplitude is velocity, ##\frac{dy}{dt}=##velocity of particle

nil1996
#4
Oct17-13, 02:07 AM
P: 296
Standing waves

Lets consider a string oscillating in fundamental frequency. In the wave equation if i put t=0 the i will get a snapshot of the wave in which all particles will be at their amplitudes. Now if i differentiate the equation that is y=Asinkx i will get something like [itex]\frac{dy}{dx}[/itex]=Akcoskx and i think this will be the rate of change of amplitude on the string. Isn't it right?
nil1996
#5
Oct17-13, 02:13 AM
P: 296
Quote Quote by NihalSh View Post
rate of change of amplitude is velocity, ##\frac{dy}{dt}=##velocity of particle
I want to say how much the amplitude changes as i move forward on x-axis.
NihalSh
#6
Oct17-13, 02:17 AM
P: 199
Quote Quote by nil1996 View Post
I want to say how much the amplitude changes as i move forward on x-axis.
Yes, you can say that!!


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