# Period of a Traveling Wave

• Noctix
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.

## 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.

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 $y(x)= y_0 sin(2\pi (x/\lambda)$.

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

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 $y(x)= y_0 sin(2\pi (x/\lambda)$.

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

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.