The relationship between wavelength and velocity is given by the equation;

The question gives us the velocity of the wave and its frequency. Using these values, we can solve for the wavelength.

For a pendulum on a string, the period at which it oscillates is:

Period is the reciprocal of frequency.

Calculate the frequency of oscillation.

The only parameter that the frequency depends on is the length . Decreasing length increases frequency. 

In this question, we're given the wavelength of light in a vaccuum. Since we know that the speed of light in a vaccuum is equal to , we can first calculate the frequency of the light, and then use this value to calculate its period.

To begin with, we'll need to make use of the following equation to solve for frequency.

Then, using this value, we can calculate the period by noting that the period is the inverse of frequency.

And for completion's sake, it is worth noting that the period refers to the amount of time it takes for one wavelength to pass, which in this case is a very, very small fraction of a second!

In order to calculate the period , we need to find the frequency, , at which the waves hit the pier. We are told that  waves hit within a  window. Therefore,

. We can then calculate the period  from this information.

The equation for the period of a pendulum is as follows:  When quadrupling the length, the square root of four can be taken out which doubles the period. 

Since the frequencies produced, differ by  we know that the fundamental frequency must be the difference. This is because the fundamental is the very first frequency and the lowest one that can be produced. 

Therefore the correct answer is .

The buoy moves a total of . From the problem, you know the buoy moves a total of  with every wavelength (10 meters up and 10 meters coming back down). This means that in 20 minutes, the buoy went through  cycles. In order to find the frequency, you divide the total amount of cycles over the total amount of time in seconds that passed:

To answer this question, it's important to have an understanding of the interrelationship between wavelength and period. Also, because we're told that this is a light wave, it's also essential that we know the speed at which light travels.

First, we can show an equation that relates wavelength and wave speed.

Moreover, we can relate the frequency of a wave to its period, both of which are inversely related to each other.

Using these two expressions, we can combine them into the following expression.

Next, we can rearrange the equation in order to isolate for the variable representing the period of the wave.

Lastly, we just need to plug in the value for wavelength given to us in the question stem, along with the speed of light, to obtain our answer.

What this answer tells us is that it will take  in order for a single wavelength of light to cross a given point - a very, very short amount of time!

Frequency is simply represent as the inverse of Period as represented below

where f is frequency and T is period. To solve the equation for period we just reverse the inverse relation