Why don't humans perceive waves as twice the frequency they are?Why do I hear beats through headphones only at low frequencies?How small can you be and still hear?Deriving the group velocity of a wave produced by some basic cosine waves with unequal amplitudesWhich is has the highest (greatest) sound intensity - Sine, Square or Sawtooth waveform?Why do we hear the square of the wave?How are beats formed when frequencies combine?Why the frequency is specified as 1KHz in the definition of threshold of audibility?Multivariable Chain-Rule in Wave-Energy EquationsIs my understanding of standing wave resonance satisfactory in this exercise?Where do pure tones occur in nature, besides harmonics?
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Why don't humans perceive waves as twice the frequency they are?
Why do I hear beats through headphones only at low frequencies?How small can you be and still hear?Deriving the group velocity of a wave produced by some basic cosine waves with unequal amplitudesWhich is has the highest (greatest) sound intensity - Sine, Square or Sawtooth waveform?Why do we hear the square of the wave?How are beats formed when frequencies combine?Why the frequency is specified as 1KHz in the definition of threshold of audibility?Multivariable Chain-Rule in Wave-Energy EquationsIs my understanding of standing wave resonance satisfactory in this exercise?Where do pure tones occur in nature, besides harmonics?
.everyoneloves__top-leaderboard:empty,.everyoneloves__mid-leaderboard:empty,.everyoneloves__bot-mid-leaderboard:empty margin-bottom:0;
$begingroup$
I was looking at how beats work. You use a amplitude wave $A = cosleft(2pi f_1xright) + cosleft(2pi f_2xright) = 2cosleft(frac2pi xleft(f_1-f_2right)2right)cosleft(frac2pi xleft(f_1+f_2right)2right)$ (frequencies $f_1$ and $f_2$).
According to Wikipedia, "Because the human ear is not sensitive to the phase of a sound, only its amplitude or intensity, only the magnitude of the envelope is heard". So obviously the audible frequency is twice the envelope (since you're squaring it) and you get $$f_audible = f_1-f_2$$and not half that.
Now consider a regular cosine wave $A = cos(2pi f_T)$ with frequency $f_T$. Taking the magnitude (as wikipedia says, i.e. by squaring A) gives you an audible frequency of $$2f_T$$... so do people hear frequencies as twice what they are in their amplitude wave?
visible-light waves acoustics
asked 8 hours ago
Mondo DukeMondo Duke
183 bronze badges
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Mondo Duke is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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add a comment |
$begingroup$
I was looking at how beats work. You use a amplitude wave $A = cosleft(2pi f_1xright) + cosleft(2pi f_2xright) = 2cosleft(frac2pi xleft(f_1-f_2right)2right)cosleft(frac2pi xleft(f_1+f_2right)2right)$ (frequencies $f_1$ and $f_2$).
According to Wikipedia, "Because the human ear is not sensitive to the phase of a sound, only its amplitude or intensity, only the magnitude of the envelope is heard". So obviously the audible frequency is twice the envelope (since you're squaring it) and you get $$f_audible = f_1-f_2$$and not half that.
Now consider a regular cosine wave $A = cos(2pi f_T)$ with frequency $f_T$. Taking the magnitude (as wikipedia says, i.e. by squaring A) gives you an audible frequency of $$2f_T$$... so do people hear frequencies as twice what they are in their amplitude wave?
visible-light waves acoustics
asked 8 hours ago
Mondo DukeMondo Duke
183 bronze badges
New contributor
Mondo Duke is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
2
$begingroup$
What is the connection of this question to the "visible-light" tag?
$endgroup$
– The Photon
6 hours ago
$begingroup$
If they did, how could you measure it?
$endgroup$
– immibis
23 mins ago
add a comment |
$begingroup$
I was looking at how beats work. You use a amplitude wave $A = cosleft(2pi f_1xright) + cosleft(2pi f_2xright) = 2cosleft(frac2pi xleft(f_1-f_2right)2right)cosleft(frac2pi xleft(f_1+f_2right)2right)$ (frequencies $f_1$ and $f_2$).
According to Wikipedia, "Because the human ear is not sensitive to the phase of a sound, only its amplitude or intensity, only the magnitude of the envelope is heard". So obviously the audible frequency is twice the envelope (since you're squaring it) and you get $$f_audible = f_1-f_2$$and not half that.
Now consider a regular cosine wave $A = cos(2pi f_T)$ with frequency $f_T$. Taking the magnitude (as wikipedia says, i.e. by squaring A) gives you an audible frequency of $$2f_T$$... so do people hear frequencies as twice what they are in their amplitude wave?
visible-light waves acoustics
asked 8 hours ago
Mondo DukeMondo Duke
183 bronze badges
New contributor
Mondo Duke is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
I was looking at how beats work. You use a amplitude wave $A = cosleft(2pi f_1xright) + cosleft(2pi f_2xright) = 2cosleft(frac2pi xleft(f_1-f_2right)2right)cosleft(frac2pi xleft(f_1+f_2right)2right)$ (frequencies $f_1$ and $f_2$).
According to Wikipedia, "Because the human ear is not sensitive to the phase of a sound, only its amplitude or intensity, only the magnitude of the envelope is heard". So obviously the audible frequency is twice the envelope (since you're squaring it) and you get $$f_audible = f_1-f_2$$and not half that.
Now consider a regular cosine wave $A = cos(2pi f_T)$ with frequency $f_T$. Taking the magnitude (as wikipedia says, i.e. by squaring A) gives you an audible frequency of $$2f_T$$... so do people hear frequencies as twice what they are in their amplitude wave?
visible-light waves acoustics
visible-light waves acoustics
asked 8 hours ago
Mondo DukeMondo Duke
183 bronze badges
New contributor
Mondo Duke is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 8 hours ago
Mondo DukeMondo Duke
183 bronze badges
New contributor
Mondo Duke is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 8 hours ago
Mondo DukeMondo Duke
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New contributor
Mondo Duke is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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asked 8 hours ago
Mondo DukeMondo Duke
183 bronze badges
asked 8 hours ago
Mondo DukeMondo Duke
183 bronze badges
183 bronze badges
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Mondo Duke is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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Check out our Code of Conduct.
2
$begingroup$
What is the connection of this question to the "visible-light" tag?
$endgroup$
– The Photon
6 hours ago
$begingroup$
If they did, how could you measure it?
$endgroup$
– immibis
23 mins ago
add a comment |
2
$begingroup$
What is the connection of this question to the "visible-light" tag?
$endgroup$
– The Photon
6 hours ago
$begingroup$
If they did, how could you measure it?
$endgroup$
– immibis
23 mins ago
2
2
$begingroup$
What is the connection of this question to the "visible-light" tag?
$endgroup$
– The Photon
6 hours ago
$begingroup$
What is the connection of this question to the "visible-light" tag?
$endgroup$
– The Photon
6 hours ago
$begingroup$
If they did, how could you measure it?
$endgroup$
– immibis
23 mins ago
$begingroup$
If they did, how could you measure it?
$endgroup$
– immibis
23 mins ago
add a comment |
2 Answers
2
active
oldest
votes
$begingroup$
Humans hear the correct perceptive signal for a sound wave of that frequency.
We really can't say much more than that. The psychology of acoustics are very complicated and could fill volumes.
It's closer to say we have cells which act resonant at a specific frequency. Our brain identifies which cells are resonating at any point in time, and constructs the signal from that. Our brains receive information that cell A or cell B is signalling. The association between those neural signals and frequencies is a learned response that we pick up early on, as an infant or perhaps even in the womb.
answered 8 hours ago
Cort AmmonCort Ammon
26.4k4 gold badges55 silver badges89 bronze badges
$endgroup$
$begingroup$
Yes. The frequencies are mapped to different distances in the cochlea. Only for low frequencies is there a relation between the action potentials and the phase of the wave. This plays a role in binaural direction sensing.
$endgroup$
– Pieter
8 hours ago
$begingroup$
Ok now I understand that sound is really subjective to how our cells perceive it. I'm still a bit confused -- I know humans hear sound waves when there are compressions and expansions in our ears, and we can't tell the difference between the two. A sound wave of frequency 1 wave per second is defined as looking like a peak/trough sine wave (or a compression and then an expansion in a second). But since we can't tell the difference between compression and expansion, won't our ears feel this frequency "1" wave as happening twice per second (i.e. an actual frequency of "2" signals per second)
$endgroup$
– Mondo Duke
7 hours ago
$begingroup$
@MondoDuke A sine wave of 100 Hz causes movements of the basilar membrane at a different position than a sine wave of 200 Hz. Different hair cells are stimulated, different "threads" in the auditory nerve start firing. (But if you want to experience something weird, listen with headphones to binaural beats.)
$endgroup$
– Pieter
7 hours ago
1
$begingroup$
We don't "sense" every cycle in the way you're thinking about it. A nerve fiber which is used in detecting 2kHz does not fire twice as fast as a nerve fiber which is used to detect 1kHz. Both fibers transmit something more akin to "here's how much power there is where my cells are at," and the cells are structured to do a fourier transform of sorts.
$endgroup$
– Cort Ammon
4 hours ago
$begingroup$
Aren't beats different than tones though? Isn't this what the OP is asking about?
$endgroup$
– Aaron Stevens
2 hours ago
add a comment |
$begingroup$
So obviously the audible frequency is twice the envelope
Sorry, that's wrong. If you play two tones (say 440Hz and 267Hz) , you simply hear two tones at two different frequencies and you have two excitations at different spots on the basilar membrane and two different set of nerves firing. You don't hear the envelope at all, they just sound like two steady state tones.
"Beats" only happen when you have two frequencies that are VERY close together, say 237Hz and 238 Hz. In this case your ear can't resolve the frequency difference anymore but your hear a single tone at 237.5 Hz that's amplitude modulated at 1 Hz.
Taking the magnitude (as wikipedia says, i.e. by squaring A) gives you
an audible frequency of 2fT
No. You can square the amplitude to estimate power or energy but there is no mechanism that would square the actual waveform . If you play 100 Hz, you hear 100Hz, that's all there is to it.
answered 4 hours ago
HilmarHilmar
9294 silver badges5 bronze badges
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2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Humans hear the correct perceptive signal for a sound wave of that frequency.
We really can't say much more than that. The psychology of acoustics are very complicated and could fill volumes.
It's closer to say we have cells which act resonant at a specific frequency. Our brain identifies which cells are resonating at any point in time, and constructs the signal from that. Our brains receive information that cell A or cell B is signalling. The association between those neural signals and frequencies is a learned response that we pick up early on, as an infant or perhaps even in the womb.
answered 8 hours ago
Cort AmmonCort Ammon
26.4k4 gold badges55 silver badges89 bronze badges
$endgroup$
$begingroup$
Yes. The frequencies are mapped to different distances in the cochlea. Only for low frequencies is there a relation between the action potentials and the phase of the wave. This plays a role in binaural direction sensing.
$endgroup$
– Pieter
8 hours ago
$begingroup$
Ok now I understand that sound is really subjective to how our cells perceive it. I'm still a bit confused -- I know humans hear sound waves when there are compressions and expansions in our ears, and we can't tell the difference between the two. A sound wave of frequency 1 wave per second is defined as looking like a peak/trough sine wave (or a compression and then an expansion in a second). But since we can't tell the difference between compression and expansion, won't our ears feel this frequency "1" wave as happening twice per second (i.e. an actual frequency of "2" signals per second)
$endgroup$
– Mondo Duke
7 hours ago
$begingroup$
@MondoDuke A sine wave of 100 Hz causes movements of the basilar membrane at a different position than a sine wave of 200 Hz. Different hair cells are stimulated, different "threads" in the auditory nerve start firing. (But if you want to experience something weird, listen with headphones to binaural beats.)
$endgroup$
– Pieter
7 hours ago
1
$begingroup$
We don't "sense" every cycle in the way you're thinking about it. A nerve fiber which is used in detecting 2kHz does not fire twice as fast as a nerve fiber which is used to detect 1kHz. Both fibers transmit something more akin to "here's how much power there is where my cells are at," and the cells are structured to do a fourier transform of sorts.
$endgroup$
– Cort Ammon
4 hours ago
$begingroup$
Aren't beats different than tones though? Isn't this what the OP is asking about?
$endgroup$
– Aaron Stevens
2 hours ago
add a comment |
$begingroup$
Humans hear the correct perceptive signal for a sound wave of that frequency.
We really can't say much more than that. The psychology of acoustics are very complicated and could fill volumes.
It's closer to say we have cells which act resonant at a specific frequency. Our brain identifies which cells are resonating at any point in time, and constructs the signal from that. Our brains receive information that cell A or cell B is signalling. The association between those neural signals and frequencies is a learned response that we pick up early on, as an infant or perhaps even in the womb.
answered 8 hours ago
Cort AmmonCort Ammon
26.4k4 gold badges55 silver badges89 bronze badges
$endgroup$
$begingroup$
Yes. The frequencies are mapped to different distances in the cochlea. Only for low frequencies is there a relation between the action potentials and the phase of the wave. This plays a role in binaural direction sensing.
$endgroup$
– Pieter
8 hours ago
$begingroup$
Ok now I understand that sound is really subjective to how our cells perceive it. I'm still a bit confused -- I know humans hear sound waves when there are compressions and expansions in our ears, and we can't tell the difference between the two. A sound wave of frequency 1 wave per second is defined as looking like a peak/trough sine wave (or a compression and then an expansion in a second). But since we can't tell the difference between compression and expansion, won't our ears feel this frequency "1" wave as happening twice per second (i.e. an actual frequency of "2" signals per second)
$endgroup$
– Mondo Duke
7 hours ago
$begingroup$
@MondoDuke A sine wave of 100 Hz causes movements of the basilar membrane at a different position than a sine wave of 200 Hz. Different hair cells are stimulated, different "threads" in the auditory nerve start firing. (But if you want to experience something weird, listen with headphones to binaural beats.)
$endgroup$
– Pieter
7 hours ago
1
$begingroup$
We don't "sense" every cycle in the way you're thinking about it. A nerve fiber which is used in detecting 2kHz does not fire twice as fast as a nerve fiber which is used to detect 1kHz. Both fibers transmit something more akin to "here's how much power there is where my cells are at," and the cells are structured to do a fourier transform of sorts.
$endgroup$
– Cort Ammon
4 hours ago
$begingroup$
Aren't beats different than tones though? Isn't this what the OP is asking about?
$endgroup$
– Aaron Stevens
2 hours ago
add a comment |
$begingroup$
Humans hear the correct perceptive signal for a sound wave of that frequency.
We really can't say much more than that. The psychology of acoustics are very complicated and could fill volumes.
It's closer to say we have cells which act resonant at a specific frequency. Our brain identifies which cells are resonating at any point in time, and constructs the signal from that. Our brains receive information that cell A or cell B is signalling. The association between those neural signals and frequencies is a learned response that we pick up early on, as an infant or perhaps even in the womb.
answered 8 hours ago
Cort AmmonCort Ammon
26.4k4 gold badges55 silver badges89 bronze badges
$endgroup$
Humans hear the correct perceptive signal for a sound wave of that frequency.
We really can't say much more than that. The psychology of acoustics are very complicated and could fill volumes.
It's closer to say we have cells which act resonant at a specific frequency. Our brain identifies which cells are resonating at any point in time, and constructs the signal from that. Our brains receive information that cell A or cell B is signalling. The association between those neural signals and frequencies is a learned response that we pick up early on, as an infant or perhaps even in the womb.
answered 8 hours ago
Cort AmmonCort Ammon
26.4k4 gold badges55 silver badges89 bronze badges
answered 8 hours ago
Cort AmmonCort Ammon
26.4k4 gold badges55 silver badges89 bronze badges
answered 8 hours ago
Cort AmmonCort Ammon
26.4k4 gold badges55 silver badges89 bronze badges
answered 8 hours ago
Cort AmmonCort Ammon
26.4k4 gold badges55 silver badges89 bronze badges
26.4k4 gold badges55 silver badges89 bronze badges
$begingroup$
Yes. The frequencies are mapped to different distances in the cochlea. Only for low frequencies is there a relation between the action potentials and the phase of the wave. This plays a role in binaural direction sensing.
$endgroup$
– Pieter
8 hours ago
$begingroup$
Ok now I understand that sound is really subjective to how our cells perceive it. I'm still a bit confused -- I know humans hear sound waves when there are compressions and expansions in our ears, and we can't tell the difference between the two. A sound wave of frequency 1 wave per second is defined as looking like a peak/trough sine wave (or a compression and then an expansion in a second). But since we can't tell the difference between compression and expansion, won't our ears feel this frequency "1" wave as happening twice per second (i.e. an actual frequency of "2" signals per second)
$endgroup$
– Mondo Duke
7 hours ago
$begingroup$
@MondoDuke A sine wave of 100 Hz causes movements of the basilar membrane at a different position than a sine wave of 200 Hz. Different hair cells are stimulated, different "threads" in the auditory nerve start firing. (But if you want to experience something weird, listen with headphones to binaural beats.)
$endgroup$
– Pieter
7 hours ago
1
$begingroup$
We don't "sense" every cycle in the way you're thinking about it. A nerve fiber which is used in detecting 2kHz does not fire twice as fast as a nerve fiber which is used to detect 1kHz. Both fibers transmit something more akin to "here's how much power there is where my cells are at," and the cells are structured to do a fourier transform of sorts.
$endgroup$
– Cort Ammon
4 hours ago
$begingroup$
Aren't beats different than tones though? Isn't this what the OP is asking about?
$endgroup$
– Aaron Stevens
2 hours ago
add a comment |
$begingroup$
Yes. The frequencies are mapped to different distances in the cochlea. Only for low frequencies is there a relation between the action potentials and the phase of the wave. This plays a role in binaural direction sensing.
$endgroup$
– Pieter
8 hours ago
$begingroup$
Ok now I understand that sound is really subjective to how our cells perceive it. I'm still a bit confused -- I know humans hear sound waves when there are compressions and expansions in our ears, and we can't tell the difference between the two. A sound wave of frequency 1 wave per second is defined as looking like a peak/trough sine wave (or a compression and then an expansion in a second). But since we can't tell the difference between compression and expansion, won't our ears feel this frequency "1" wave as happening twice per second (i.e. an actual frequency of "2" signals per second)
$endgroup$
– Mondo Duke
7 hours ago
$begingroup$
@MondoDuke A sine wave of 100 Hz causes movements of the basilar membrane at a different position than a sine wave of 200 Hz. Different hair cells are stimulated, different "threads" in the auditory nerve start firing. (But if you want to experience something weird, listen with headphones to binaural beats.)
$endgroup$
– Pieter
7 hours ago
1
$begingroup$
We don't "sense" every cycle in the way you're thinking about it. A nerve fiber which is used in detecting 2kHz does not fire twice as fast as a nerve fiber which is used to detect 1kHz. Both fibers transmit something more akin to "here's how much power there is where my cells are at," and the cells are structured to do a fourier transform of sorts.
$endgroup$
– Cort Ammon
4 hours ago
$begingroup$
Aren't beats different than tones though? Isn't this what the OP is asking about?
$endgroup$
– Aaron Stevens
2 hours ago
$begingroup$
Yes. The frequencies are mapped to different distances in the cochlea. Only for low frequencies is there a relation between the action potentials and the phase of the wave. This plays a role in binaural direction sensing.
$endgroup$
– Pieter
8 hours ago
$begingroup$
Yes. The frequencies are mapped to different distances in the cochlea. Only for low frequencies is there a relation between the action potentials and the phase of the wave. This plays a role in binaural direction sensing.
$endgroup$
– Pieter
8 hours ago
$begingroup$
Ok now I understand that sound is really subjective to how our cells perceive it. I'm still a bit confused -- I know humans hear sound waves when there are compressions and expansions in our ears, and we can't tell the difference between the two. A sound wave of frequency 1 wave per second is defined as looking like a peak/trough sine wave (or a compression and then an expansion in a second). But since we can't tell the difference between compression and expansion, won't our ears feel this frequency "1" wave as happening twice per second (i.e. an actual frequency of "2" signals per second)
$endgroup$
– Mondo Duke
7 hours ago
$begingroup$
Ok now I understand that sound is really subjective to how our cells perceive it. I'm still a bit confused -- I know humans hear sound waves when there are compressions and expansions in our ears, and we can't tell the difference between the two. A sound wave of frequency 1 wave per second is defined as looking like a peak/trough sine wave (or a compression and then an expansion in a second). But since we can't tell the difference between compression and expansion, won't our ears feel this frequency "1" wave as happening twice per second (i.e. an actual frequency of "2" signals per second)
$endgroup$
– Mondo Duke
7 hours ago
$begingroup$
@MondoDuke A sine wave of 100 Hz causes movements of the basilar membrane at a different position than a sine wave of 200 Hz. Different hair cells are stimulated, different "threads" in the auditory nerve start firing. (But if you want to experience something weird, listen with headphones to binaural beats.)
$endgroup$
– Pieter
7 hours ago
$begingroup$
@MondoDuke A sine wave of 100 Hz causes movements of the basilar membrane at a different position than a sine wave of 200 Hz. Different hair cells are stimulated, different "threads" in the auditory nerve start firing. (But if you want to experience something weird, listen with headphones to binaural beats.)
$endgroup$
– Pieter
7 hours ago
1
1
$begingroup$
We don't "sense" every cycle in the way you're thinking about it. A nerve fiber which is used in detecting 2kHz does not fire twice as fast as a nerve fiber which is used to detect 1kHz. Both fibers transmit something more akin to "here's how much power there is where my cells are at," and the cells are structured to do a fourier transform of sorts.
$endgroup$
– Cort Ammon
4 hours ago
$begingroup$
We don't "sense" every cycle in the way you're thinking about it. A nerve fiber which is used in detecting 2kHz does not fire twice as fast as a nerve fiber which is used to detect 1kHz. Both fibers transmit something more akin to "here's how much power there is where my cells are at," and the cells are structured to do a fourier transform of sorts.
$endgroup$
– Cort Ammon
4 hours ago
$begingroup$
Aren't beats different than tones though? Isn't this what the OP is asking about?
$endgroup$
– Aaron Stevens
2 hours ago
$begingroup$
Aren't beats different than tones though? Isn't this what the OP is asking about?
$endgroup$
– Aaron Stevens
2 hours ago
add a comment |
$begingroup$
So obviously the audible frequency is twice the envelope
Sorry, that's wrong. If you play two tones (say 440Hz and 267Hz) , you simply hear two tones at two different frequencies and you have two excitations at different spots on the basilar membrane and two different set of nerves firing. You don't hear the envelope at all, they just sound like two steady state tones.
"Beats" only happen when you have two frequencies that are VERY close together, say 237Hz and 238 Hz. In this case your ear can't resolve the frequency difference anymore but your hear a single tone at 237.5 Hz that's amplitude modulated at 1 Hz.
Taking the magnitude (as wikipedia says, i.e. by squaring A) gives you
an audible frequency of 2fT
No. You can square the amplitude to estimate power or energy but there is no mechanism that would square the actual waveform . If you play 100 Hz, you hear 100Hz, that's all there is to it.
answered 4 hours ago
HilmarHilmar
9294 silver badges5 bronze badges
$endgroup$
add a comment |
$begingroup$
So obviously the audible frequency is twice the envelope
Sorry, that's wrong. If you play two tones (say 440Hz and 267Hz) , you simply hear two tones at two different frequencies and you have two excitations at different spots on the basilar membrane and two different set of nerves firing. You don't hear the envelope at all, they just sound like two steady state tones.
"Beats" only happen when you have two frequencies that are VERY close together, say 237Hz and 238 Hz. In this case your ear can't resolve the frequency difference anymore but your hear a single tone at 237.5 Hz that's amplitude modulated at 1 Hz.
Taking the magnitude (as wikipedia says, i.e. by squaring A) gives you
an audible frequency of 2fT
No. You can square the amplitude to estimate power or energy but there is no mechanism that would square the actual waveform . If you play 100 Hz, you hear 100Hz, that's all there is to it.
answered 4 hours ago
HilmarHilmar
9294 silver badges5 bronze badges
$endgroup$
add a comment |
$begingroup$
So obviously the audible frequency is twice the envelope
Sorry, that's wrong. If you play two tones (say 440Hz and 267Hz) , you simply hear two tones at two different frequencies and you have two excitations at different spots on the basilar membrane and two different set of nerves firing. You don't hear the envelope at all, they just sound like two steady state tones.
"Beats" only happen when you have two frequencies that are VERY close together, say 237Hz and 238 Hz. In this case your ear can't resolve the frequency difference anymore but your hear a single tone at 237.5 Hz that's amplitude modulated at 1 Hz.
Taking the magnitude (as wikipedia says, i.e. by squaring A) gives you
an audible frequency of 2fT
No. You can square the amplitude to estimate power or energy but there is no mechanism that would square the actual waveform . If you play 100 Hz, you hear 100Hz, that's all there is to it.
answered 4 hours ago
HilmarHilmar
9294 silver badges5 bronze badges
$endgroup$
So obviously the audible frequency is twice the envelope
Sorry, that's wrong. If you play two tones (say 440Hz and 267Hz) , you simply hear two tones at two different frequencies and you have two excitations at different spots on the basilar membrane and two different set of nerves firing. You don't hear the envelope at all, they just sound like two steady state tones.
"Beats" only happen when you have two frequencies that are VERY close together, say 237Hz and 238 Hz. In this case your ear can't resolve the frequency difference anymore but your hear a single tone at 237.5 Hz that's amplitude modulated at 1 Hz.
Taking the magnitude (as wikipedia says, i.e. by squaring A) gives you
an audible frequency of 2fT
No. You can square the amplitude to estimate power or energy but there is no mechanism that would square the actual waveform . If you play 100 Hz, you hear 100Hz, that's all there is to it.
answered 4 hours ago
HilmarHilmar
9294 silver badges5 bronze badges
answered 4 hours ago
HilmarHilmar
9294 silver badges5 bronze badges
answered 4 hours ago
HilmarHilmar
9294 silver badges5 bronze badges
answered 4 hours ago
HilmarHilmar
9294 silver badges5 bronze badges
9294 silver badges5 bronze badges
add a comment |
add a comment |
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2
$begingroup$
What is the connection of this question to the "visible-light" tag?
$endgroup$
– The Photon
6 hours ago
$begingroup$
If they did, how could you measure it?
$endgroup$
– immibis
23 mins ago