Why are both positive and negative amplitudes counted as maxima in a sine curve?

[ZaZu]

Homework Statement

Hello there,

There is a question that says :

...etc...the metal is then moved towards the hardboard. In moving 6.4cm, four further maxima are observed. Calculate the wavelength of the ...etc...

Now I know how to solve it, and got the answer.
(sine curve)
But why do we count the amplitudes both below in the and above the axis as maxima ?
I thought the maximum points are all the points above the x axis, and the minimum points are the minimum points ??!

The Attempt at a Solution

All I did was : 4 max = 2\lambda .. But these 4 maximum points are both ABOVE and BELOW the x-axis for a sine curve.

Then 2\lambda=6.4cm
\lambda=3.2cmIf you need me to explain my question exactly, please ask me to clarify.

 

[astrorob]

Hi ZaZu,

I'm not 100% of what you're asking so if I'm telling you something you already know - forgive me.

I presume the experiment involves counting how many maxima OR minima of a standing wave propagating between two fixed points, the distance between which you know already.

In this case you're really only after counting either the number of consecutive maxima or minima, not both, for this is the definition of wavelength.

 

[ZaZu]

Hi ZaZu,

I'm not 100% of what you're asking so if I'm telling you something you already know - forgive me.

I presume the experiment involves counting how many maxima OR minima of a standing wave propagating between two fixed points, the distance between which you know already.

In this case you're really only after counting either the number of consecutive maxima or minima, not both, for this is the definition of wavelength.

Yes that's exactly what I mean, but in our class we did the following :

http://img404.imageshack.us/img404/2170/image352.th.jpg Is this correct ?

 

[Hootenanny]

The amplitude is the magnitude of the displacement from the equilibrium position of the oscillating variable. It doesn't matter whether this displacement is positive or negative since the amplitude is the magnitude of the displacement.

For example, consider the function y = sin(x). A maximum value of y occurs as sin(pi/2) = 1 and a minimum value of y occurs at sin(-pi/2) = -1. However, in both cases the amplitude is 1, since A = |y|. Since the amplitude, by definition is non-negative, it's minimum value is clearly the minimum of y > 0.

Do you follow?

 

[astrorob]

Yes it is.

Note the 2 on the RHS corresponding to 2 consecutive peaks/troughs of maxima OR minima.

 

[ZaZu]

The amplitude is the magnitude of the displacement from the equilibrium position of the oscillating variable. It doesn't matter whether this displacement is positive or negative since the amplitude is the magnitude of the displacement.

For example, consider the function y = sin(x). A maximum value of y occurs as sin(pi/2) = 1 and a minimum value of y occurs at sin(-pi/2) = -1. However, in both cases the amplitude is 1, since A = |y|. Since the amplitude, by definition is non-negative, it's minimum value is clearly the minimum of y > 0.

Do you follow?

So in my question, I can say that both the minimum AND maximum points are the MAXIMA ??

 

[ZaZu]

Yes it is.

Note the 2 on the RHS corresponding to 2 consecutive peaks/troughs of maxima OR minima.

Oh alright, so its concluded that both the crests and troughs can be considered the maximum points ?

 

[astrorob]

Careful here. They correspond to points of maximum amplitude but in regards to their physical positions, they must be differentiated (i.e. by the use of maxima/minima).

 

[ZaZu]

Careful here. They correspond to points of maximum amplitude but in regards to their physical positions, they must be differentiated (i.e. by the use of maxima/minima).

Oh I see, great !

Its clearer now :)

Thanks a lot astrorob and Hootenanny :D :D :D