# AP Physics 1 : Frequency and Period

## Example Questions

### Example Question #1 : Frequency And Period

What is the wavelength of a  wave if its velocity is ?

Explanation:

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.

### Example Question #2 : Frequency And Period

A pendulum of length  with a ball of mass  is released at an angle  away from the equilibrium point. Which of the following adjustments will result in an increase in frequency of oscillation?

Increasing the initial angle

Increasing the length

Decreasing the length

Decreasing the ball's mass

Increasing the ball's mass

Decreasing the length

Explanation:

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.

### Example Question #3 : Frequency And Period

The wavelength of a ray of light travelling through a vaccuum is . What is the period of this wave?

Explanation:

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!

### Example Question #4 : Frequency And Period

Waves are hitting the side of a pier in a regular fashion. During 1 minute,  waves that hit the side of the pier. Calculate the period  of the waves during this time in seconds.

Cannot be determined.

Explanation:

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.

### Example Question #5 : Frequency And Period

How does the period of a pendulum react to its length quadrupling?

Is cut in half.

Decreases by .

Increases twofold.

Increases by .

Increases twofold.

Explanation:

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.

### Example Question #6 : Frequency And Period

A string produces the following frequencies: , , , and .

What is the fundamental frequency of this string?

Explanation:

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 .

### Example Question #7 : Frequency And Period

A buoy is rocking in the ocean when a storm hits. From the lowest point to the highest point, the buoy goes up a total of . Over the last 20 minutes, the buoy has moved up and down a total of

What is the frequency of the buoy's oscillation?

Explanation:

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:

### Example Question #8 : Frequency And Period

If the wavelength of a light wave is , what is the period of this wave?

Explanation:

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!

### Example Question #9 : Frequency And Period

The frequency of a sound wave traveling through water at  is record to be , what is the period of the wave?