Waves, Sound, and Light - High School Physics
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Two piano strings are supposed to be vibrating at 
, but a piano tuner hears 4 beats every 3 seconds when they are played together. If one of the piano strings is vibrating correctly at 
, what must be the frequency of the other?
Two piano strings are supposed to be vibrating at 
With the information provided we can determine the frequency of the beats.
This means that the string of the piano could either be this much higher or lower than the 
string.
With the information provided we can determine the frequency of the beats.
This means that the string of the piano could either be this much higher or lower than the 
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The siren of a police car at rest emits a frequency of about 
. What frequency will you hear if you are at rest and the police car moves 
away from you?
The siren of a police car at rest emits a frequency of about 
This is an example of the doppler effect. In this case the source is moving away from a stationary observer. Therefore the corresponding equation is
This is an example of the doppler effect. In this case the source is moving away from a stationary observer. Therefore the corresponding equation is
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Two waves, each with an amplitude of 
are superimposed with constructive interference such that they are in phase. What is the resultant amplitude?
Two waves, each with an amplitude of 
When two waves are superimposed, the interference can either be constructive or destructive. In this case, the interference is constructive and the waves are in phase, which means we add the amplitudes together.
Since each wave has an amplitude of 
, our new amplitude will be 
.
When two waves are superimposed, the interference can either be constructive or destructive. In this case, the interference is constructive and the waves are in phase, which means we add the amplitudes together.
Since each wave has an amplitude of 
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Two waves, one with an amplitude of 
and the other of 
are superimposed with destructive interference. What is the resultant amplitude?
Two waves, one with an amplitude of 
When two waves are superimposed, the interference can be either constructive or destructive. In this case the interference is destructive, which means our resultant amplitude will be the difference of the two given amplitudes.
That means our new amplitude will be 
.
When two waves are superimposed, the interference can be either constructive or destructive. In this case the interference is destructive, which means our resultant amplitude will be the difference of the two given amplitudes.
That means our new amplitude will be 
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A piano tuner hears one beat every 
when trying to adjust two strings, one of which is sounding 
. How far off in frequency is the other string?
A piano tuner hears one beat every 
We can calculate the frequency of the beat using the equation
This is the beat frequency which means that the other string is off by 
either higher or lower.
We can calculate the frequency of the beat using the equation
This is the beat frequency which means that the other string is off by 
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Two identical waves are superimposed with destructive interference. What will happen to the resulting wave?
Two identical waves are superimposed with destructive interference. What will happen to the resulting wave?
When two waves are superimposed with destructive interference, they cancel each other out. Since these two waves are identical, they will completely cancel each other out and there will be no wave. It will be still.
When two waves are superimposed with destructive interference, they cancel each other out. Since these two waves are identical, they will completely cancel each other out and there will be no wave. It will be still.
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Resonance in a system, such as a string fixed on both ends, occurs when
Resonance in a system, such as a string fixed on both ends, occurs when
When we think about a violin or a guitar string that is being plucked, there are a variety of waves of different frequencies that will travel along the string and be reflected back at the ends. Most interfere with each other and disappear. The few that don’t will remain. These are called the resonant frequencies. These frequencies create standing waves on the string. If the frequencies do not align, they will interfere and die out. However, if the frequency is the same standing waves occur and resonance occurs. We can also see this in a tuning fork. If we have two tuning forks of the same frequency and we strike the first and bring it near the second, it will begin to resonant as well as the air molecules strike the second fork causing it to vibrate. If we do the same test with two different frequency forks, nothing will occur.
When we think about a violin or a guitar string that is being plucked, there are a variety of waves of different frequencies that will travel along the string and be reflected back at the ends. Most interfere with each other and disappear. The few that don’t will remain. These are called the resonant frequencies. These frequencies create standing waves on the string. If the frequencies do not align, they will interfere and die out. However, if the frequency is the same standing waves occur and resonance occurs. We can also see this in a tuning fork. If we have two tuning forks of the same frequency and we strike the first and bring it near the second, it will begin to resonant as well as the air molecules strike the second fork causing it to vibrate. If we do the same test with two different frequency forks, nothing will occur.
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Two pure tones are sounded together and a particular beat frequency is heard. What happens to the beat frequency if the frequency on one of the tones is increased?
Two pure tones are sounded together and a particular beat frequency is heard. What happens to the beat frequency if the frequency on one of the tones is increased?
Beats occur due to the interference of two different frequencies that are occurring at the same time. These beats are repetitive patterns of loud and soft interference that happen at regular intervals. To calculate the beat frequency, simply take the difference of the two frequencies. This means that if the higher frequency is increased, the beat frequency is increasing and is getting farther away from the lower frequency. If the lower frequency is increased, the beat frequency is decreasing as it is getting closer to the higher frequency and therefore reducing the difference between the two.
Beats occur due to the interference of two different frequencies that are occurring at the same time. These beats are repetitive patterns of loud and soft interference that happen at regular intervals. To calculate the beat frequency, simply take the difference of the two frequencies. This means that if the higher frequency is increased, the beat frequency is increasing and is getting farther away from the lower frequency. If the lower frequency is increased, the beat frequency is decreasing as it is getting closer to the higher frequency and therefore reducing the difference between the two.
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An ambulance turns on its siren as it is driving away from you. What happens to the sound pitch?
An ambulance turns on its siren as it is driving away from you. What happens to the sound pitch?
The Doppler effect states that the frequency of sound increases as it approaches you and decreases as it goes away from you.
Since it is going away from you, the pitch of the sound will appear to get lower.
The Doppler effect states that the frequency of sound increases as it approaches you and decreases as it goes away from you.
Since it is going away from you, the pitch of the sound will appear to get lower.
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A wave has a frequency of 
. What is its period?
A wave has a frequency of 
The relationship between frequency and period is 
.
Plug in our given value:
The relationship between frequency and period is 
Plug in our given value:
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After exercising, Jane takes her pulse. She realizes that her heart is beating rapidly, approximately four beats every second. What is the period of her elevated heart rate?
After exercising, Jane takes her pulse. She realizes that her heart is beating rapidly, approximately four beats every second. What is the period of her elevated heart rate?
When you see a relationship like "times every second" or "once per hour," these are hints you are looking at a frequency. Frequency is, effectively, how often something happens. If it happens four times per second, then we know how often it happens. The units "per second" are equivalent to Hertz.
The relationship between frequency and period is 
.
Since our given frequency was four beats per second, or 
, we can solve for the period.
This means that her heart beats once every 
seconds.
When you see a relationship like "times every second" or "once per hour," these are hints you are looking at a frequency. Frequency is, effectively, how often something happens. If it happens four times per second, then we know how often it happens. The units "per second" are equivalent to Hertz.
The relationship between frequency and period is 
Since our given frequency was four beats per second, or 
This means that her heart beats once every 
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A wave oscillates with a speed of 
and has a wavelength of 
. What is the frequency of the wave?
A wave oscillates with a speed of 
The equation for velocity in terms of wavelength and frequency is 
.
We are given the velocity and the wavelength. Using these values, we can solve for the frequency.
The equation for velocity in terms of wavelength and frequency is 
We are given the velocity and the wavelength. Using these values, we can solve for the frequency.
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What is the wavelength of the wave above?
What is the wavelength of the wave above?
The wavelength of a wave is defined as the distance from a point on the wave to the same point on the wave (crest to crest or trough to trough). The distance between peaks is 
.
The wavelength of a wave is defined as the distance from a point on the wave to the same point on the wave (crest to crest or trough to trough). The distance between peaks is 
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What is the amplitude of the wave above?
What is the amplitude of the wave above?
The amplitude of wave is defined as the distance the wave displaces from the equilibrium point. In this case, the wave displaces 
from the axis (the equilibrium point).
The amplitude of wave is defined as the distance the wave displaces from the equilibrium point. In this case, the wave displaces 
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A wave with a constant velocity doubles its frequency. What happens to its wavelength?
A wave with a constant velocity doubles its frequency. What happens to its wavelength?
The relationship between velocity, frequency, and wavelength is:
In this case we're given a scenario where 
and 
. The velocities equal each other because the problem states it has a constant velocity. Therefore we can set these equations equal to each other:
Notice that the f's cancel out:
Divide both sides by two:
The relationship between velocity, frequency, and wavelength is:
In this case we're given a scenario where 
Notice that the f's cancel out:
Divide both sides by two:
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Two notes are played simultaneously. One of them has a period of 
and the other has a period of 
. Which one has a longer wavelength?
Two notes are played simultaneously. One of them has a period of 
The relationship between frequency and wavelength determines the velocity:
The frequency is the inverse of the period. We can substitute this into the equation above.
In the question, both of the notes are played at the same time in the same location, so they both should have the same velocity. We can set the equation for each tone equal to each other.
We are told that 
. Substitute into our equation.
We can cancel the period from each side of the equation, leaving the relationship between the two wavelengths.
The wavelength of the first wave is equal to half the wavelength of the second. This means that the wavelength for the tone with a longer period will have a longer wavelength as well.
The relationship between frequency and wavelength determines the velocity:
The frequency is the inverse of the period. We can substitute this into the equation above.
In the question, both of the notes are played at the same time in the same location, so they both should have the same velocity. We can set the equation for each tone equal to each other.
We are told that 
We can cancel the period from each side of the equation, leaving the relationship between the two wavelengths.
The wavelength of the first wave is equal to half the wavelength of the second. This means that the wavelength for the tone with a longer period will have a longer wavelength as well.
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A student attaches one end of a Slinky to the top of a table. She holds the other end in her hand, stretches it to a length 
, and then moves it back and forth to send a wave down the Slinky. If she next moves her hand faster while keeping the length of the Slinky the same, how does the wavelength down the slinky change?
A student attaches one end of a Slinky to the top of a table. She holds the other end in her hand, stretches it to a length 
The speed of the wave along the Slinky depends on the mass of the Slinky itself and the tension caused by stretching it. Since both of these things have not changed, the wave speed remains constant.
The wave speed is equal to the wavelength multiplied by the frequency.
Since she is moving her hand faster, the frequency has increased. Since the velocity has not changed, an increase in the frequency would decrease the wavelength
The speed of the wave along the Slinky depends on the mass of the Slinky itself and the tension caused by stretching it. Since both of these things have not changed, the wave speed remains constant.
The wave speed is equal to the wavelength multiplied by the frequency.
Since she is moving her hand faster, the frequency has increased. Since the velocity has not changed, an increase in the frequency would decrease the wavelength
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Resonance in a system, such as a string fixed at both ends, occurs when
Resonance in a system, such as a string fixed at both ends, occurs when
The frequency at which standing waves are produced is known as the resonant frequencies. When two objects are brought near each other, and they both make standing waves at the same frequency, there is resonance in the system. For example, if you have two tuning forks of the same note, you can tap one and bring it close (but not touch) the other. Then if you silence the first tuning fork and listen, you will hear the second fork ringing as well because it vibrates at the same frequency.
The frequency at which standing waves are produced is known as the resonant frequencies. When two objects are brought near each other, and they both make standing waves at the same frequency, there is resonance in the system. For example, if you have two tuning forks of the same note, you can tap one and bring it close (but not touch) the other. Then if you silence the first tuning fork and listen, you will hear the second fork ringing as well because it vibrates at the same frequency.
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A radio station broadcasts at a frequency of 
. If the broadcast is an electromagnetic wave, then what is its wavelength?
A radio station broadcasts at a frequency of 
The relationship between wavelength and frequency is given by the equation 
, where 
is the wavelength, 
is the speed of light, and 
is frequency.
We are given the values for frequency and the speed of light, allowing us to solve for the wavelength.
The relationship between wavelength and frequency is given by the equation 
We are given the values for frequency and the speed of light, allowing us to solve for the wavelength.
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In seismology, the 
wave is a transverse wave. As an 
wave travels through the Earth, the relative motion between the 
wave and the particles is
In seismology, the 
Transverse waves are waves whose particles travel perpendicular to the direction that the wave itself is traveling. Electromagnetic waves are another example of transverse waves.
Transverse waves are waves whose particles travel perpendicular to the direction that the wave itself is traveling. Electromagnetic waves are another example of transverse waves.
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