Waves - MCAT Physical
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What phenomenon can occur with light, but not sound?
What phenomenon can occur with light, but not sound?
Sound is a longitudinal wave, while light is a transverse wave. Polarization requires the direction of the wave to be perpendicular to the direction of propogation; only light can do this. Doppler effect, refraction, and interference occur in both wave types.
Sound is a longitudinal wave, while light is a transverse wave. Polarization requires the direction of the wave to be perpendicular to the direction of propogation; only light can do this. Doppler effect, refraction, and interference occur in both wave types.
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Which statement is not true for all waves?
Which statement is not true for all waves?
The speed of sound is dependent on the temperature of the transmitting medium. The speed of light is not.
The speed of sound is dependent on the temperature of the transmitting medium. The speed of light is not.
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Sound traveling at a velocity, V1, through a certain medium will travel at what velocity through a medium of twice the density?
Sound traveling at a velocity, V1, through a certain medium will travel at what velocity through a medium of twice the density?
The speed of sound depends on both the medium’s density and resistance to compression. We do not have enough information to solve for V2 in terms of V1.
The speed of sound depends on both the medium’s density and resistance to compression. We do not have enough information to solve for V2 in terms of V1.
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What is the frequency of a typical soundwave traveling at 340m/s with a wavelength of 40mm?
What is the frequency of a typical soundwave traveling at 340m/s with a wavelength of 40mm?
Using the equation 
we can find the frequency of the soundwave.
Using the equation
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At a local concert, a speaker is set up to produce low-pitched base sounds with a frequency range of 20Hz to 200Hz, which can be modeled as sine waves. In a simplified model, the sound waves the speaker produces can be modeled as a cylindrical pipe with one end closed that travel through the air at a velocity of 
, where T is the temperature in °C.
As a person walks towards the speaker, the frequency he or she hears __________.
At a local concert, a speaker is set up to produce low-pitched base sounds with a frequency range of 20Hz to 200Hz, which can be modeled as sine waves. In a simplified model, the sound waves the speaker produces can be modeled as a cylindrical pipe with one end closed that travel through the air at a velocity of
As a person walks towards the speaker, the frequency he or she hears __________.
This question is asking us how the frequency changes when one object moves directly towards another; thus, this is a Doppler effect problem. Remembering back to our Doppler effect formula, we know that
, where f is the frequency heard by the recipient (the person at the concert), vr is the velocity of the receiver, vs is the velocity of the source, and f0 is the original frequency.
In our case, the speaker is not moving, so vs is zero. vr is positive when the person is walking towards the speaker, so the frequency heard will be higher than the original frequency.
This question is asking us how the frequency changes when one object moves directly towards another; thus, this is a Doppler effect problem. Remembering back to our Doppler effect formula, we know that
In our case, the speaker is not moving, so vs is zero. vr is positive when the person is walking towards the speaker, so the frequency heard will be higher than the original frequency.
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A sound source with a frequency of 790Hz moves away from a stationary observer at a rate of 15m/s. What frequency does the observer hear?
The speed of sound is 340m/s.
A sound source with a frequency of 790Hz moves away from a stationary observer at a rate of 15m/s. What frequency does the observer hear?
The speed of sound is 340m/s.
In this scenario the Doppler effect is described by the following equation.
Using the values from the problem, we know that vo is zero and vf is 15m/s. v is 340m/s and fs is 790Hz.
In this scenario the Doppler effect is described by the following equation.
Using the values from the problem, we know that vo is zero and vf is 15m/s. v is 340m/s and fs is 790Hz.
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A fire truck emits an 880Hz siren. As the truck approaches an obeserver on the sidewalk, he perceives the pitch to be 950Hz. Approximately what pitch does he hear after the truck passes and is moving away? Assume the truck's velocity remains constant, and that the velocity of sound in air is 340m/s.
A fire truck emits an 880Hz siren. As the truck approaches an obeserver on the sidewalk, he perceives the pitch to be 950Hz. Approximately what pitch does he hear after the truck passes and is moving away? Assume the truck's velocity remains constant, and that the velocity of sound in air is 340m/s.
The equation for Doppler effect is 
, where the + sign applies when the source and observer are moving farther apart, and the - sign applies when they are moving closer together. In these equations, v is the speed of sound, 340m/s, 
is the frequency of sound emitted by the source, 
is the freqency perceived by the observer, and 
is the relative velocity between the source and observer.
We can apply this equation to the first part of the motion, as the truck moves closer to the observer, to solve for the velocity of the truck.
Now we can plug this velocity into the equation again for when the truck moves farther away from the observer and solve for 
.
The equation for Doppler effect is
We can apply this equation to the first part of the motion, as the truck moves closer to the observer, to solve for the velocity of the truck.
Now we can plug this velocity into the equation again for when the truck moves farther away from the observer and solve for
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Which of the following best describes the effect of the Doppler shift on the appearance of stars moving towards Earth?
Which of the following best describes the effect of the Doppler shift on the appearance of stars moving towards Earth?
The Doppler shift equation for light is 
, where f is the source frequency, f' is the observed frequency, v is the relative velocity between source and observer, and c is the speed of light.
When the source and observer are moving closer together, v is positive, so the observed frequency is greater than the source frequency. Greater frequency also implies shorter wavelength, so visible light is shifted towards the blue end of the spectrum.
The Doppler shift equation for light is
When the source and observer are moving closer together, v is positive, so the observed frequency is greater than the source frequency. Greater frequency also implies shorter wavelength, so visible light is shifted towards the blue end of the spectrum.
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A fire truck emitting a siren at 
moves at 
towards a jogger. The jogger is moving at 
towards the fire truck. Take the speed of sound to be 
.
At what frequency does the jogger perceive the siren?
A fire truck emitting a siren at
At what frequency does the jogger perceive the siren?
In order to solve this problem we must know how to utilize the Doppler formula.
is the velocity of the observer and 
is the velocity of the source. Notice that the frequency must increase as the observer and source move closer, and therefore the plus sign is used in the numerator and the minus sign is used in the denominator. Had the jogger been moving away from the fire truck, the subtraction function would be used in both the top and bottom.
In this case we see that the source is the fire truck, moving at 
, and the observer is the jogger, moving at 
. By plugging these numbers into the formula and 
for 
, we find the perceived frequency or 
to be 
.
In order to solve this problem we must know how to utilize the Doppler formula.
In this case we see that the source is the fire truck, moving at
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At a local concert, a speaker is set up to produce low-pitched base sounds with a frequency range of 20Hz to 200Hz, which can be modeled as sine waves. In a simplified model, the sound waves the speaker produces can be modeled as a cylindrical pipe with one end closed that travel through the air at a velocity of 
, where T is the temperature in °C.
A person runs away from the speaker at 3m/s, while it creates a 200Hz sound wave. What frequency does he or she hear?
Use 340m/s for the speed of sound.
At a local concert, a speaker is set up to produce low-pitched base sounds with a frequency range of 20Hz to 200Hz, which can be modeled as sine waves. In a simplified model, the sound waves the speaker produces can be modeled as a cylindrical pipe with one end closed that travel through the air at a velocity of
A person runs away from the speaker at 3m/s, while it creates a 200Hz sound wave. What frequency does he or she hear?
Use 340m/s for the speed of sound.
This question is asking us how the frequency changes when one object moves directly away from another; thus, this is a Doppler effect problem. Remembering back to our Doppler effect formula, we know that
, where f is the frequency heard by the recipient (the person at the concert), vr is the velocity of the receiver, vs is the velocity of the source, and f0 is the original frequency.
In our case, the speaker is not moving, so vs is zero. vr is negative when the person is walking towards the speaker, so the frequency heard will be lower than the original frequency. We can calculate the heard frequency using our equation.
This question is asking us how the frequency changes when one object moves directly away from another; thus, this is a Doppler effect problem. Remembering back to our Doppler effect formula, we know that
In our case, the speaker is not moving, so vs is zero. vr is negative when the person is walking towards the speaker, so the frequency heard will be lower than the original frequency. We can calculate the heard frequency using our equation.
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The source of a sound moves away from the listener. The listener has the impression that the source is __________.
The source of a sound moves away from the listener. The listener has the impression that the source is __________.
The formula for the Doppler effect is:
Only frequency of the sound is affected by the Doppler effect; velocity and amplitude remain unchanged. When the source is moving away from the observer the velocity of the source is added to the speed of light.
This increases the value of the denominator, decreasing the value of the observed frequency. Frequency corresponds to pitch or tone; a lower observed frequency will result in a lower observed pitch.
The formula for the Doppler effect is:
Only frequency of the sound is affected by the Doppler effect; velocity and amplitude remain unchanged. When the source is moving away from the observer the velocity of the source is added to the speed of light.
This increases the value of the denominator, decreasing the value of the observed frequency. Frequency corresponds to pitch or tone; a lower observed frequency will result in a lower observed pitch.
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You are jogging on the sidewalk at a rate of 
. A police car behind you is patrolling at a rate of 
when it turns on its siren. If the siren has a frequency of 
, is the frequency you perceive higher or lower than the frequency emitted?
You are jogging on the sidewalk at a rate of
The doppler effect states that if two objects are moving closer together, perceived frequencies for emitted waves will be higher. If you are jogging away from the car at 
, but the car is traveling at 
, the overall distance between you and the siren is decreasing. You will hear a higher frequency than what the siren is emitting.
The numerator is subtracted when the observer moves away from the source. The denominator is subtracted when the source moves toward the observer. In this problem both terms would be subtracted, but the denominator would be decreased by more than the numerator. This would result in a fraction greater than one, and an overall increase in the final frequency.
The doppler effect states that if two objects are moving closer together, perceived frequencies for emitted waves will be higher. If you are jogging away from the car at
The numerator is subtracted when the observer moves away from the source. The denominator is subtracted when the source moves toward the observer. In this problem both terms would be subtracted, but the denominator would be decreased by more than the numerator. This would result in a fraction greater than one, and an overall increase in the final frequency.
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A star emits visible color at 
. If the star is moving away from a stationary observer, which of the following cannot be the wavelength observed?
A star emits visible color at
The Doppler effect accounts for observed frequency versus actual frequency emitted by a sound or light source. The equation for the Doppler effect is:
The numerator terms are summed when the observer moves toward the source, and the denominator terms are summed when the source moves away from the observer. In this question, we know that the source moves away from the observer; therefore, the observed frequency will be less than the actual frequency because the denominator in the equation will increase.
The question, however, asks about wavelength. If the frequency decreases, then the wavelength must increase according to the equation:
Velocity will remain constant (the speed of light). Any change in frequency will cause a change in wavelength via their direct relationship in the given equation.
The Doppler effect accounts for observed frequency versus actual frequency emitted by a sound or light source. The equation for the Doppler effect is:
The numerator terms are summed when the observer moves toward the source, and the denominator terms are summed when the source moves away from the observer. In this question, we know that the source moves away from the observer; therefore, the observed frequency will be less than the actual frequency because the denominator in the equation will increase.
The question, however, asks about wavelength. If the frequency decreases, then the wavelength must increase according to the equation:
Velocity will remain constant (the speed of light). Any change in frequency will cause a change in wavelength via their direct relationship in the given equation.
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You observe several stars in the distance with varying colors. Which of the following stars would have the highest surface temperature?
You observe several stars in the distance with varying colors. Which of the following stars would have the highest surface temperature?
The light portion of the electromagnetic spectrum, from lowest to highest frequency, is red, orange, yellow, green, blue, indigo, violet (ROYGBIV).
Frequency is proportional to temperature, and wavelength is inversely proportional to frequency. Since the energy level corresponds with the temperature, objects that emit a higher frequency and shorter wavelength photon will have higher energy. This corresponds with violet, as it is the highest frequency (shortest wavelength) of visible light
The light portion of the electromagnetic spectrum, from lowest to highest frequency, is red, orange, yellow, green, blue, indigo, violet (ROYGBIV).
Frequency is proportional to temperature, and wavelength is inversely proportional to frequency. Since the energy level corresponds with the temperature, objects that emit a higher frequency and shorter wavelength photon will have higher energy. This corresponds with violet, as it is the highest frequency (shortest wavelength) of visible light
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Two cars approach each other at 
when one car starts to beep its horn at a frequency of 475Hz. What is the wavelength of the horn as heard by the other driver?
Two cars approach each other at
The Doppler equation is:
.
Because the cars are approaching each other, the frquency heard will be increased. This fundamental knowledge allows you to determine the signs of the equation. The top of the fraction will be addition and the bottom will be subtraction to make a coefficient greater than 1.
Use the given values to solve:
Now that we know the frequency, we can solve for the wavelength:
The Doppler equation is:
Because the cars are approaching each other, the frquency heard will be increased. This fundamental knowledge allows you to determine the signs of the equation. The top of the fraction will be addition and the bottom will be subtraction to make a coefficient greater than 1.
Use the given values to solve:
Now that we know the frequency, we can solve for the wavelength:
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If the first overtone of a sound wave in a pipe with one end open and one end closed has a frequency of 300Hz, what is the frequency of the second overtone?
If the first overtone of a sound wave in a pipe with one end open and one end closed has a frequency of 300Hz, what is the frequency of the second overtone?
In an open-closed pipe, we get only odd harmonics, since there must always be a displacement node at the closed end and a displacement antinode at the open end. So, the first overtone is the same as the third harmonic, which has 
. Similarly, the second overtone is the fifth harmonic, which has 
. Using the given value of 
in the first overtone to be 300Hz, we find 
and 
.
In an open-closed pipe, we get only odd harmonics, since there must always be a displacement node at the closed end and a displacement antinode at the open end. So, the first overtone is the same as the third harmonic, which has
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A string of length 2.5m is struck producing a harmonic. The wavelength produced is 1.25m. Which harmonic is the string vibrating at?
A string of length 2.5m is struck producing a harmonic. The wavelength produced is 1.25m. Which harmonic is the string vibrating at?
A harmonic is a standing wave that has certain points (nodes) which do not go through any displacement, and certain points (antinodes) that are moving through maximum displacement during the wave's resonation.
Wavelength is related to harmonic on a string fixed at both ends through the formula 
, where 
is the length of the string and 
is the number harmonic. By plugging in the given length and wavelength, we can solve for 
.
The string must be vibrating at the fourth harmonic.
A harmonic is a standing wave that has certain points (nodes) which do not go through any displacement, and certain points (antinodes) that are moving through maximum displacement during the wave's resonation.
Wavelength is related to harmonic on a string fixed at both ends through the formula
The string must be vibrating at the fourth harmonic.
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At a local concert, a speaker is set up to produce low-pitched base sounds with a frequency range of 20Hz to 200Hz, which can be modeled as sine waves. In a simplified model, the sound waves the speaker produces can be modeled as a cylindrical pipe with one end closed that travel through the air at a velocity of 
, where T is the temperature in °C.
How are the first three harmonics of the base speaker designated?
At a local concert, a speaker is set up to produce low-pitched base sounds with a frequency range of 20Hz to 200Hz, which can be modeled as sine waves. In a simplified model, the sound waves the speaker produces can be modeled as a cylindrical pipe with one end closed that travel through the air at a velocity of
How are the first three harmonics of the base speaker designated?
First, notice that the paragraph above tells us that the wave can be modeled as a pipe with one end closed. This is in contrast to the other possibility, where the wave is modeled as a pipe with two ends open. It is critical to recognize this difference, as the definition of sequential harmonics and the formula used to calculate them changes depending on whether both ends are open or not. In the situation where one end is closed, the harmonics are odd numbers, meaning that the first three harmonics are 1st, 3rd, and 5th. In the situation where both ends are open or both ends are closed, the harmonics are sequential, meaning that the first three harmonics are 1st, 2nd, and 3rd.
First, notice that the paragraph above tells us that the wave can be modeled as a pipe with one end closed. This is in contrast to the other possibility, where the wave is modeled as a pipe with two ends open. It is critical to recognize this difference, as the definition of sequential harmonics and the formula used to calculate them changes depending on whether both ends are open or not. In the situation where one end is closed, the harmonics are odd numbers, meaning that the first three harmonics are 1st, 3rd, and 5th. In the situation where both ends are open or both ends are closed, the harmonics are sequential, meaning that the first three harmonics are 1st, 2nd, and 3rd.
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Each of the following types of waves experience polarization except __________.
Each of the following types of waves experience polarization except __________.
Polarization is the property that allows tansverse waves to oscillate in multiple orientations. A transverse wave can oscillate, for example, in either the xy-plane or the yz-plane.
Sound waves are longitudinal, and thus do no experience polarization as medium is displaced in one direction only. A longitudinal wave will travel in only one dimension via compression and rarefraction.
Polarization is the property that allows tansverse waves to oscillate in multiple orientations. A transverse wave can oscillate, for example, in either the xy-plane or the yz-plane.
Sound waves are longitudinal, and thus do no experience polarization as medium is displaced in one direction only. A longitudinal wave will travel in only one dimension via compression and rarefraction.
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At a local concert, a speaker is set up to produce low-pitched base sounds with a frequency range of 20Hz to 200Hz, which can be modeled as sine waves. In a simplified model, the sound waves the speaker produces can be modeled as a cylindrical pipe with one end closed that travel through the air at a velocity of 
, where T is the temperature in °C.
What is the closest distance a person could be standing away from the speaker in order to hear the loudest fundamental frequency of a 1.2m wavelength wave at the concert?
At a local concert, a speaker is set up to produce low-pitched base sounds with a frequency range of 20Hz to 200Hz, which can be modeled as sine waves. In a simplified model, the sound waves the speaker produces can be modeled as a cylindrical pipe with one end closed that travel through the air at a velocity of
What is the closest distance a person could be standing away from the speaker in order to hear the loudest fundamental frequency of a 1.2m wavelength wave at the concert?
This question asks us to incorporate information we learned in the pre-question text and new information in the question. First, we are told that we are looking to calculate a distance where maximal sound is heard, in other words, where the amplitude is at its maximum. This only occurs at an anti-node.
Additionally, we know that the speaker can be modeled as a one-end closed pipe, meaning that the wavelengths of the harmonics are calculated as 
.
In a one-end closed pipe model, each harmonic ends with maximal amplitude, so we can find L (the length of the pipe, i.e. where the person standing would hear maximal sound), as we know the fundamental harmonic has n = 1.
This question asks us to incorporate information we learned in the pre-question text and new information in the question. First, we are told that we are looking to calculate a distance where maximal sound is heard, in other words, where the amplitude is at its maximum. This only occurs at an anti-node.
Additionally, we know that the speaker can be modeled as a one-end closed pipe, meaning that the wavelengths of the harmonics are calculated as
In a one-end closed pipe model, each harmonic ends with maximal amplitude, so we can find L (the length of the pipe, i.e. where the person standing would hear maximal sound), as we know the fundamental harmonic has n = 1.
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