What does the A stand for in this equation?

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    Amplitude
In summary, the A in the equation y=A\sin{(kx-t\omega)} stands for amplitude. The relationship between k and the wavelength of the wave is k=\frac{2\pi}{\lambda}. The relationship between \omega and the time period T of the wave is T = \frac{2 \pi}{\omega}.
  • #1
BLUE_CHIP
What does the [tex]A[/tex] stand for in the equation:

[tex]y=A\sin{(kx-t\omega)}[/tex]



CHEERS :)
 
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  • #2
Amplitude.

- Warren
 
  • #3
max value of the displacement from the mean position
 
  • #4
thanks :)

but could you answer this

whats the relationship between [tex]k[/tex] and the wavelength of the wave
 
  • #5
[tex]k=\frac{2\pi}{\lambda}[/tex]
 
  • #6
Think about it. If x is the displacement along a taught string, the wavelength of a wave on that string is the distance between successive crests or troughs.

All sine waves repeat every 2 pi radians.

When [itex]x = \lambda[/itex], you want the argument to be [itex]2 \pi[/itex].

Try rewriting the first term (the term with the x) as:

[tex]\frac{2 \pi x}{\lambda}[/tex]

You'll see that when [itex]x = \lambda[/itex], the entire expression is [itex]2 \pi[/itex] -- exactly one period. This is the right expression.

Therefore, if you want to simplify that expression by bringing in a new symbol k, k must be

[tex]k = \frac{2 \pi}{\lambda}[/tex]

- Warren
 
Last edited:
  • #7
Score! thanks Boudoir
 
  • #8
Bummer hit a brick wall again. check this out:

for the equation [tex]y=A\sin{(kx-t\omega)}[/tex] find a relationship between [tex]\omega[/tex] and the time period [tex]T[/tex] of the wave.

when [tex]t=T[/tex] [tex]y=0[/tex] and [tex]x=0[/tex]

therefore:

[tex]A\sin{(-T\omega)}=0[/tex]

but then what?
 
  • #9
Don't you have a textbook?

[tex]\omega = 2 \pi f[/tex]

[tex]T = \frac{1}{f}[/tex]

[tex]T = \frac{2 \pi}{\omega}[/tex]

- Warren
 
  • #10
Originally posted by chroot
Don't you have a textbook?


- Warren

I think you're doing his homework for him.
 
  • #11
I don't find it as Homework.

Anyway He is reaching the conclusions and that's the bottom line
 
  • #12
Thanks :smile: saved my life.
 

What is amplitude in an equation?

Amplitude in an equation is the measure of the maximum deviation of a function from its central value. It is the distance from the center line of a graph to the highest or lowest point of a wave.

How is amplitude represented in an equation?

Amplitude is usually represented by the variable "A" in an equation. It can also be represented by the symbol "peak-to-peak amplitude", which is the distance between the highest and lowest points of a wave.

What is the significance of amplitude in an equation?

The amplitude of a wave is directly related to its energy. A higher amplitude indicates a greater amount of energy, while a lower amplitude indicates a lower amount of energy. Amplitude also affects the loudness or brightness of a wave.

How is amplitude related to frequency in an equation?

Amplitude and frequency are inversely related in an equation. This means that as the frequency of a wave increases, the amplitude decreases, and vice versa.

How can amplitude be calculated in an equation?

Amplitude can be calculated by finding the difference between the highest and lowest points of a wave. It can also be calculated using the formula A = (maximum value - minimum value)/2.

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