All AP Physics 2 Resources
Example Questions
Example Question #34 : Waves
Which of the following parameters will increase when the frequency of a sound wave is decreased?
I. Period
II. Wavelength
III. Amplitude
I, II, and III
I and III
II and III
I and II
II only
I and II
For this question, we need to consider wave characteristics. Specifically, we need to determine how a decrease in the frequency of a wave will alter its wavelength, period, and amplitude.
First, let's consider the period of the wave. The period is defined as the amount of time needed for one complete cycle of the wave to occur. Conversely, frequency is defined as the number of wave cycles completed within a given time frame. As such, period and frequency are inversely related to one another, as the following expression shows:
Therefore, the period of the wave will certainly increase as the frequency of the wave decreases.
Now, let's take a look at wavelength. We need to recall the speed of a wave is defined in terms of its wavelength and frequency according to the following equation:
As we can see from the above equation, frequency is inversely related to wavelength, just as it is with period. Therefore, as the frequency of a wave decreases, the wavelength will indeed rise.
Finally, let's look at amplitude. The amplitude of a wave is the magnitude of the difference between the extremes of the wave and its equilibrium position. In transverse waves, such as a rope, the amplitude is the maximum displacement of a particle of that rope from its equilibrium position in the direction perpendicular to the propagation of the wave. In longitudinal waves, such as sound, the amplitude is the maximum displacement of the medium from its equilibrium position in the direction parallel to the propagation of the wave.
Because there is no relationship between amplitude and frequency, a decrease in a wave's frequency will have no effect on that wave's amplitude. Thus, for this question, only wavelength and period are increased due to a decreased frequency.
Example Question #7 : Other Wave Concepts
Determine the frequency of electromagnetic radiation of wavelength .
Using the following equation:
Converting to and plugging in values:
Example Question #41 : Waves
Suppose that a vibrating string fixed at both ends has one harmonic at a wavelength of followed by another harmonic at . What is the length of this string?
We're given the wavelengths of two subsequent harmonics of a string fixed at both ends, and we're asked to solve for the length of the string.
First, we must used the equation for a standing wave that has a node at both ends.
Before we can solve for the length of the string, we need to first solve for the value of . We can do this by considering the wavelength of the two harmonics as follows.
Now, since the length of the string for either harmonic is the same length, we can set the two expressions above equal to each other.
Now, we can solve for the variable .
Now that we have the value for , we can plug this value into the original expression to calculate the length of the string.
Example Question #42 : Waves
A team of engineers decides to drill a hole all the way through the diameter of the Earth. A wave (with wavelength ) is sent through the hole to a receiver on the other end who, upon receiving the wave, immediately sends the wave back through the hole to the original sender. The original sender says it took the wave exactly half a second to return to him after he sent it. The hole is approximately long. What is the frequency of the wave?
We are given the distance the wave travels (twice the Earth's diameter), and the time it took for it to travel that distance. Using this we can determine the wave's speed.
Now we can use to find the frequency.
-wavelength
-frequency
*Side note-Let's assume the index of refraction of the hole is constant. In order for the wave to travel at that speed, the index of refraction must be .
Example Question #42 : Waves
For open pipes, the formula for wave patterns at any given time can be given by a Fourier Sine Series which is given as the infinite sum:
when is an integer, and is the length of the pipe. Each individual value of is called a harmonic.
What is the wavelength of the fundamental harmonic?
The fundamental harmonic is when , and therefore the wavelength can be given by:
, where is the frequency of the fundamental harmonic.
Example Question #241 : Ap Physics 2
As a wave propagates from one medium to another, the speed decreases by a factor of two (halves). Which of the following is true about the wave in the second medium?
Frequency doubles
Wavelength doubles
Frequency halves
Wavelength halves
No change
Wavelength halves
, where is the velocity of the wave, is the wavelength of the wave, and is the frequency. When the speed is cut in half, the frequency does not change! However, that means the wavelength is directly proportional to the speed and will also be cut in half.
Example Question #41 : Waves
Which of the following waves can propagate in a vacuum?
I. Sound waves
II. X-ray waves
III. Radio waves
II and III
II only
III only
I only
I, II, and III
II and III
In a vacuum, waves that travel at the speed of light propagate. Therefore, we need to determine which of the three types of waves have that speed. All parts of the electromagnetic spectrum travel at the speed of light (so X-ray and radio are true). Sound waves travel at the speed of sound, which is less than the speed of light. Therefore, that one is incorrect.
Example Question #13 : Other Wave Concepts
What is defined by the term wavelength?
The number of seconds it takes for one full wave to pass.
How fast the waves travel in one second.
How far a wave travels in one second.
The number of waves going past in one second.
From the crest of one wave to the subsequent crest of the next wave.
From the crest of one wave to the subsequent crest of the next wave.
Wavelength and frequency are inversely related. We define the wavelength of a wave as the distance between the two subsequent waves measured at the same point on the wave. Therefore, we can measure from crest to crest or trough to trough.
Example Question #46 : Waves
If a sound is increased by , by how much does the intensity of that sound change?
It becomes times as intense
It becomes times as intense
It becomes times as intense
It becomes times as intense
It becomes times as intense
It becomes times as intense
In this question, we're told that a certain sound is increases by decibals. We're asked to find how the intensity of the sound changes as a result.
To answer this, we need to understand that there is a logarithmic relationship between decibals and intensity. This can be shown by the following expression that relates the two.
We can rearrange this equation to isolate the intensity ratio of after and before.
This shows that the intensity increases by a factor of .
As a side note, for every decibals added, the intensity of the sound increases by a factor of .
Example Question #47 : Waves
Which of the following statements is not consistent with the wave theory of light?
A beam of light shining on a metal plate is capable of displacing electrons from the metal
A beam of light shined at a small slit with a diameter smaller than the wavelength of the light will result in a diffraction pattern
Two or more waves are able to interfere with each other, such that a new wave with different parameters is created
All of these statements are consistent with the wave theory of light
When passing from a medium that is less dense to a medium that is more dense, a light ray will bend toward the normal
A beam of light shining on a metal plate is capable of displacing electrons from the metal
This question is asking us to identify a statement that is not consistent with the wave theory of light.
In its beginning, light was traditionally viewed as being only a wave. In time, however, certain observations came to light (no pun intended) that did not agree with the wave theory. As a result, scientists needed to turn to a new theory that could account for the new observations.
This led to what is called the particle nature of light. When shining a beam of light on a metal plate, it was found that only certain frequencies of light could eject electrons from the metal. However, the wave theory of light alone could not explain this phenomenon, which came to be called the photoelectric effect. Instead, if light were to be treated like a particle, in which there are many discrete photons that behave like particles, the photoelectric effect can be adequately explained.
It's important to note, however, that this did not usurp the wave model. In fact, the wave model is able to explain several things that the particle model cannot. For instance, the diffraction, refraction, and interference of light are all consistent with the wave model, but not the particle model. Consequently, both models are valid and are invoked depending on the circumstance. This is what is known as the wave-particle duality of light.
Certified Tutor
Certified Tutor