Math Is Fun Forum

tigerfan

Member

Registered: 2007-03-09

Posts: 8

sinusoidal wave speeds????

a sinusoidal wave is described by y= (0.30)sin(0.20x-40t) what is the wave speed?

Anyone got any clues on how to solve this????

Last edited by tigerfan (2007-03-10 05:41:34)

Stanley_Marsh

Member

Registered: 2006-12-13

Posts: 345

Re: sinusoidal wave speeds????

speed = wave lengh / period (time)

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Talvon

Member

Registered: 2006-11-15

Posts: 16

Re: sinusoidal wave speeds????

omega=2pi*f (Omega=40 from your wave equation)

k (Wave number) = 0.2 - Again, lifted from wave equation

k=2pi/lambda

Use your values calculated and stick it in v=f*lambda

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: sinusoidal wave speeds????

On this one, x is just a number that varies from -infinity to + infinity to create
the static non-moving wave.  Now t is what makes the wave move, this is time.
So what you have to do is start off easier like sin(x - t), just do that one.
Now if x is in radians, then you see that for every 2pi change in t, the
wave move left or right, not sure yet by one wave-length.
The wavelength is not 0.30, that is the height of the wave from center to top or
center to bottom because sin goes from -1 to 0 to +1 to 0 to -1 and so forth.
The distance from the top of the wave to the next top or crests is 2pi for sin(x-t),
but for sin(0.2x), then the x's are not as effective since they are multiplied by 0.2, so
now x has to go five times further in order to make a wave.
So the wavelength is now 5 times 2 pi or 10pi from crest to crest (top to top).

Now that you know the size of the wave, this shouldn't matter, but it DOES, because
the 40t is being compared to the 0.20x, so like for every 40t equal to 0.2 times 10pi,
the wave moves a whole wave.  So if 40t is 10pi/5 or 2pi, then the wave moves
by 10pi. 
So 40t = 2pi when the wave moves 10pi is how I figure this to be.
So t = 2pi/40 or pi/20 seconds (perhaps seconds) when the wave goes 10pi meters maybe.
Dividing that out distance per time, and you get 10pi meters/(pi/20), and you
get 200 meters per second.
Hopefully I did that right!  Can't be sure.
But I got 200 meters per second.

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