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

This problem emphasizes the importance of being able to sift through a problem statement and pick out only the information you need to solve the problem. We are given four values, but only need two of them. If you are unable to sift through the problem effectively, you are likely to get bogged down by all the details and waste time performing unneeded calculations.

To find the speed of sound in the water, we only need one equation:

We are given the frequency of the sound and its wavelength in water. It is important to note that the frequency of a sound does not change as it enters a different medium; only the velocity and wavelength do.

Plugging in our values, we get:

If you got the answer 400 m/s, watch your units! You probably divided 340 m/s by 0.85 m, which gives you units of 1/s. That is a unit of frequency, not velocity.

In order to determine the velocity of a wave, we need to know the frequency and wavelength. From the problem statement, we know that a wave is created every 2 seconds. This is the period of the wave; therefore we can say that the frequency is:

Now we just need the wavelength. We are told that there are four full waves over a distance of 5 meters.

We can use the following formula to get the velocity:

To determine the velocity of the created waves, we need to know how quickly they cover a certain distance. The problem statement tells us that the covered distance is 800km. From the given time differences, we know that it takes 1 hour and 15 minutes to cover that distance. We will need to convert this to seconds:

Now we can calculate the speed of the waves:

For any wave,

We know that the frequency of middle C is 262 hertz, and we also know that the speed of sound is . Therefore:

Solving for wavelength yields

The equation relaing velocity, wavelength, and frequency is:

.

Solving for frequency,