Period of a Traveling Wave

In summary, at x = 15.0 cm and t = 2.00 s, the displacement of a traveling wave is 8.66 cm with an amplitude of 10.0 cm and a wavelength of 8.00 cm. Using the equation y(x,t)=y0sin2pi(x/lambda-t/period), we can determine the period of the wave to be 1.17 s, assuming the smallest positive phase angle.
  • #1
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Homework Statement


At x = 15.0 cm and t = 2.00 s, the displacement of a traveling wave is 8.66 cm. The amplitude of the wave is 10.0 cm, and its wavelength is 8.00 cm. Assume the smallest positive phase angle.
What is its period?

Homework Equations



y(x,t)=y0sin2pi(x/lambda-t/period)

The Attempt at a Solution



y(2)=10sin(8.66/8-2/T)

I don't know if I set it up right, and I don't knw how to solve the equation from here because i don't know the value of y... any and all help is greatly appreciated.
 
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  • #2
The period of the wave is the same no matter what t is so take t to be a fixed number, 0 is simplest. Then we have [itex]y(x)= y_0 sin(2\pi (x/\lambda)[/itex].

We know that the period of "sin(x)" alone is [itex]2\pi[/itex]- so that one period of [itex]sin(2\pi(x/\lambda))[/itex] will occur between [itex]2\pi(x/\lambda)= 0[/itex] and [itex]2\pi(x/\lambda)= 2\pi[/itex].
 
  • #3
HallsofIvy said:
The period of the wave is the same no matter what t is so take t to be a fixed number, 0 is simplest. Then we have [itex]y(x)= y_0 sin(2\pi (x/\lambda)[/itex].

We know that the period of "sin(x)" alone is [itex]2\pi[/itex]- so that one period of [itex]sin(2\pi(x/\lambda))[/itex] will occur between [itex]2\pi(x/\lambda)= 0[/itex] and [itex]2\pi(x/\lambda)= 2\pi[/itex].


sorry, i don't quite understand what you're saying. If we use t=0, the period is canceled out of the equation, isn't it? even if not, how do i get an answer out of your two final equations?
sorry for being slow... i haven't had trig, so this is all really new to me.
also, I should have mentioned this earlier, but I'm aiming for the answer period=1.17s
 

What is the period of a traveling wave?

The period of a traveling wave is the amount of time it takes for one complete wavelength to pass a fixed point in space. It is measured in seconds.

How is the period of a traveling wave related to its frequency?

The period of a traveling wave is inversely proportional to its frequency. This means that as the frequency increases, the period decreases, and vice versa.

Can the period of a traveling wave be changed?

No, the period of a traveling wave is dependent on the medium through which it travels and the frequency of the wave. It cannot be changed unless these factors are altered.

What is the relationship between wavelength and period in a traveling wave?

The period of a traveling wave is directly proportional to its wavelength. This means that as the wavelength increases, the period also increases, and vice versa.

How is the period of a traveling wave related to the speed of the wave?

The period of a traveling wave is inversely proportional to the speed of the wave. This means that as the speed of the wave increases, the period decreases, and vice versa.

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