Apart from the sine wave, are there any other waveshapes that could be thought of as commonly appearing “in nature”?Are there any substances that allow sound to travel better then air?Using sinusoids to represent sound wavesAre there any ways to alter frequency of wave?Why is a sine wave considered the fundamental building block of any signal? Why not some other function?Fundamentally speaking, what are all the essential factors for waves (of any nature) to exist?Are there solutions of three dimensional wave equation that are not cylindrical, spherical or plane?For a sine (or cosine) wave, how can the $kx$ be different from $omega t$?What are waves? Where does the wave equation come from?Are there pure sine waves in nature or are they a mathematical construct that helps us understand more complex phenomena?Are there any differences between the standing wave diagrams of two non-transposing instruments?
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Apart from the sine wave, are there any other waveshapes that could be thought of as commonly appearing "in nature"?
Apart from the sine wave, are there any other waveshapes that could be thought of as commonly appearing “in nature”?
Are there any substances that allow sound to travel better then air?Using sinusoids to represent sound wavesAre there any ways to alter frequency of wave?Why is a sine wave considered the fundamental building block of any signal? Why not some other function?Fundamentally speaking, what are all the essential factors for waves (of any nature) to exist?Are there solutions of three dimensional wave equation that are not cylindrical, spherical or plane?For a sine (or cosine) wave, how can the $kx$ be different from $omega t$?What are waves? Where does the wave equation come from?Are there pure sine waves in nature or are they a mathematical construct that helps us understand more complex phenomena?Are there any differences between the standing wave diagrams of two non-transposing instruments?
$begingroup$
I'm familiar with the sine wave being something that can be used to model many types of oscillation in nature (and the way that multiple sine waves can be seen as sum to produce complex waveforms, a la Fourier's theorem).
However, I'm struggling to think of any other waveforms that can be associated with phenomena in nature. Are there any, or does the sinusoid stand alone as the basic 'shape' of most naturally-occurring cyclic phenomena?
(To give another perspective on my question - when it comes to static values, there are various well-known mathematical constants such as π, e, The imaginary unit i, the golden ratio φ - but are there any well-known mathematical or physical cycle shapes, apart from the sinusoid?)
waves
asked 8 hours ago
topo mortotopo morto
1062
New contributor
topo morto is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
|
show 3 more comments
$begingroup$
I'm familiar with the sine wave being something that can be used to model many types of oscillation in nature (and the way that multiple sine waves can be seen as sum to produce complex waveforms, a la Fourier's theorem).
However, I'm struggling to think of any other waveforms that can be associated with phenomena in nature. Are there any, or does the sinusoid stand alone as the basic 'shape' of most naturally-occurring cyclic phenomena?
(To give another perspective on my question - when it comes to static values, there are various well-known mathematical constants such as π, e, The imaginary unit i, the golden ratio φ - but are there any well-known mathematical or physical cycle shapes, apart from the sinusoid?)
waves
asked 8 hours ago
topo mortotopo morto
1062
New contributor
topo morto is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
$begingroup$
The earth's orbit around the sun has had some attention from physicists.
$endgroup$
– WillO
8 hours ago
$begingroup$
Hardly anything is exactly sinusoidal. Picking nice functions for waveforms tends to be simply wanting an analytic solution, rather than that they are somehow realistic.
$endgroup$
– jacob1729
8 hours ago
$begingroup$
While we all love sin/cos and Fourier transforms, don't forget the various orthogonal polynomial bases out there, such as the Legendre, Tschebysheff, Jacobi, and Laguerre.
$endgroup$
– Jon Custer
8 hours ago
$begingroup$
@WillO in my naivety I'm seeing an orbit as effectively more or less a composition of sinusoids happening in more than one dimension at once... am I wrong to do so?
$endgroup$
– topo morto
8 hours ago
1
$begingroup$
Twisting words a bit: is it that nature always oscillates in sine waves, or is it that the thing you have chosen to define with the word "oscillate" is that which is described by sine waves, thus rejecting all natural motions which are not sine waves?
$endgroup$
– Cort Ammon
8 hours ago
|
show 3 more comments
$begingroup$
I'm familiar with the sine wave being something that can be used to model many types of oscillation in nature (and the way that multiple sine waves can be seen as sum to produce complex waveforms, a la Fourier's theorem).
However, I'm struggling to think of any other waveforms that can be associated with phenomena in nature. Are there any, or does the sinusoid stand alone as the basic 'shape' of most naturally-occurring cyclic phenomena?
(To give another perspective on my question - when it comes to static values, there are various well-known mathematical constants such as π, e, The imaginary unit i, the golden ratio φ - but are there any well-known mathematical or physical cycle shapes, apart from the sinusoid?)
waves
asked 8 hours ago
topo mortotopo morto
1062
New contributor
topo morto is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
I'm familiar with the sine wave being something that can be used to model many types of oscillation in nature (and the way that multiple sine waves can be seen as sum to produce complex waveforms, a la Fourier's theorem).
However, I'm struggling to think of any other waveforms that can be associated with phenomena in nature. Are there any, or does the sinusoid stand alone as the basic 'shape' of most naturally-occurring cyclic phenomena?
(To give another perspective on my question - when it comes to static values, there are various well-known mathematical constants such as π, e, The imaginary unit i, the golden ratio φ - but are there any well-known mathematical or physical cycle shapes, apart from the sinusoid?)
waves
waves
asked 8 hours ago
topo mortotopo morto
1062
New contributor
topo morto 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
topo mortotopo morto
1062
New contributor
topo morto 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
topo mortotopo morto
1062
New contributor
topo morto 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
topo mortotopo morto
1062
asked 8 hours ago
topo mortotopo morto
1062
1062
New contributor
topo morto is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
topo morto is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$begingroup$
The earth's orbit around the sun has had some attention from physicists.
$endgroup$
– WillO
8 hours ago
$begingroup$
Hardly anything is exactly sinusoidal. Picking nice functions for waveforms tends to be simply wanting an analytic solution, rather than that they are somehow realistic.
$endgroup$
– jacob1729
8 hours ago
$begingroup$
While we all love sin/cos and Fourier transforms, don't forget the various orthogonal polynomial bases out there, such as the Legendre, Tschebysheff, Jacobi, and Laguerre.
$endgroup$
– Jon Custer
8 hours ago
$begingroup$
@WillO in my naivety I'm seeing an orbit as effectively more or less a composition of sinusoids happening in more than one dimension at once... am I wrong to do so?
$endgroup$
– topo morto
8 hours ago
1
$begingroup$
Twisting words a bit: is it that nature always oscillates in sine waves, or is it that the thing you have chosen to define with the word "oscillate" is that which is described by sine waves, thus rejecting all natural motions which are not sine waves?
$endgroup$
– Cort Ammon
8 hours ago
|
show 3 more comments
$begingroup$
The earth's orbit around the sun has had some attention from physicists.
$endgroup$
– WillO
8 hours ago
$begingroup$
Hardly anything is exactly sinusoidal. Picking nice functions for waveforms tends to be simply wanting an analytic solution, rather than that they are somehow realistic.
$endgroup$
– jacob1729
8 hours ago
$begingroup$
While we all love sin/cos and Fourier transforms, don't forget the various orthogonal polynomial bases out there, such as the Legendre, Tschebysheff, Jacobi, and Laguerre.
$endgroup$
– Jon Custer
8 hours ago
$begingroup$
@WillO in my naivety I'm seeing an orbit as effectively more or less a composition of sinusoids happening in more than one dimension at once... am I wrong to do so?
$endgroup$
– topo morto
8 hours ago
1
$begingroup$
Twisting words a bit: is it that nature always oscillates in sine waves, or is it that the thing you have chosen to define with the word "oscillate" is that which is described by sine waves, thus rejecting all natural motions which are not sine waves?
$endgroup$
– Cort Ammon
8 hours ago
$begingroup$
The earth's orbit around the sun has had some attention from physicists.
$endgroup$
– WillO
8 hours ago
$begingroup$
The earth's orbit around the sun has had some attention from physicists.
$endgroup$
– WillO
8 hours ago
$begingroup$
Hardly anything is exactly sinusoidal. Picking nice functions for waveforms tends to be simply wanting an analytic solution, rather than that they are somehow realistic.
$endgroup$
– jacob1729
8 hours ago
$begingroup$
Hardly anything is exactly sinusoidal. Picking nice functions for waveforms tends to be simply wanting an analytic solution, rather than that they are somehow realistic.
$endgroup$
– jacob1729
8 hours ago
$begingroup$
While we all love sin/cos and Fourier transforms, don't forget the various orthogonal polynomial bases out there, such as the Legendre, Tschebysheff, Jacobi, and Laguerre.
$endgroup$
– Jon Custer
8 hours ago
$begingroup$
While we all love sin/cos and Fourier transforms, don't forget the various orthogonal polynomial bases out there, such as the Legendre, Tschebysheff, Jacobi, and Laguerre.
$endgroup$
– Jon Custer
8 hours ago
$begingroup$
@WillO in my naivety I'm seeing an orbit as effectively more or less a composition of sinusoids happening in more than one dimension at once... am I wrong to do so?
$endgroup$
– topo morto
8 hours ago
$begingroup$
@WillO in my naivety I'm seeing an orbit as effectively more or less a composition of sinusoids happening in more than one dimension at once... am I wrong to do so?
$endgroup$
– topo morto
8 hours ago
1
1
$begingroup$
Twisting words a bit: is it that nature always oscillates in sine waves, or is it that the thing you have chosen to define with the word "oscillate" is that which is described by sine waves, thus rejecting all natural motions which are not sine waves?
$endgroup$
– Cort Ammon
8 hours ago
$begingroup$
Twisting words a bit: is it that nature always oscillates in sine waves, or is it that the thing you have chosen to define with the word "oscillate" is that which is described by sine waves, thus rejecting all natural motions which are not sine waves?
$endgroup$
– Cort Ammon
8 hours ago
|
show 3 more comments
3 Answers
3
active
oldest
votes
$begingroup$
stick-slip friction cycling gives rise to a sawtooth waveform, which is nonsinusoidal- although it can be built up out of a series of sine waves by superposition.
answered 8 hours ago
niels nielsenniels nielsen
22.2k53062
$endgroup$
$begingroup$
Thanks! yes, I guess all recurring waveforms can be built up of sines, but this is a great answer as the phenomenon itself isn't really fundamentally like that (unlike, say, a body orbiting around another orbiting body)
$endgroup$
– topo morto
8 hours ago
add a comment |
$begingroup$
However, I'm struggling to think of any other waveforms that can be
associated with phenomena in nature
This one has been getting some attention recently.
Image credit
answered 6 hours ago
Alfred CentauriAlfred Centauri
49.2k350155
$endgroup$
1
$begingroup$
That looks like a sinusoidal wave, though? It's just got its amplitude and frequency changing over time.
$endgroup$
– nick012000
5 mins ago
add a comment |
$begingroup$
However, I'm struggling to think of any other waveforms that can be associated with phenomena in nature.
The motion of an ordinary pendulum of length $L$ is cyclic, but non-sinusoidal (it is only approximately sinusoidal for small angles). The exact non-sinusoidal motion is governed by the non-linear equation:
$$
fracd^2thetadt^2=-fracgLsin(theta)
$$
answered 8 hours ago
hfthft
4,1581922
$endgroup$
add a comment |
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3 Answers
3
active
oldest
votes
3 Answers
3
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
stick-slip friction cycling gives rise to a sawtooth waveform, which is nonsinusoidal- although it can be built up out of a series of sine waves by superposition.
answered 8 hours ago
niels nielsenniels nielsen
22.2k53062
$endgroup$
$begingroup$
Thanks! yes, I guess all recurring waveforms can be built up of sines, but this is a great answer as the phenomenon itself isn't really fundamentally like that (unlike, say, a body orbiting around another orbiting body)
$endgroup$
– topo morto
8 hours ago
add a comment |
$begingroup$
stick-slip friction cycling gives rise to a sawtooth waveform, which is nonsinusoidal- although it can be built up out of a series of sine waves by superposition.
answered 8 hours ago
niels nielsenniels nielsen
22.2k53062
$endgroup$
$begingroup$
Thanks! yes, I guess all recurring waveforms can be built up of sines, but this is a great answer as the phenomenon itself isn't really fundamentally like that (unlike, say, a body orbiting around another orbiting body)
$endgroup$
– topo morto
8 hours ago
add a comment |
$begingroup$
stick-slip friction cycling gives rise to a sawtooth waveform, which is nonsinusoidal- although it can be built up out of a series of sine waves by superposition.
answered 8 hours ago
niels nielsenniels nielsen
22.2k53062
$endgroup$
stick-slip friction cycling gives rise to a sawtooth waveform, which is nonsinusoidal- although it can be built up out of a series of sine waves by superposition.
answered 8 hours ago
niels nielsenniels nielsen
22.2k53062
answered 8 hours ago
niels nielsenniels nielsen
22.2k53062
answered 8 hours ago
niels nielsenniels nielsen
22.2k53062
answered 8 hours ago
niels nielsenniels nielsen
22.2k53062
22.2k53062
$begingroup$
Thanks! yes, I guess all recurring waveforms can be built up of sines, but this is a great answer as the phenomenon itself isn't really fundamentally like that (unlike, say, a body orbiting around another orbiting body)
$endgroup$
– topo morto
8 hours ago
add a comment |
$begingroup$
Thanks! yes, I guess all recurring waveforms can be built up of sines, but this is a great answer as the phenomenon itself isn't really fundamentally like that (unlike, say, a body orbiting around another orbiting body)
$endgroup$
– topo morto
8 hours ago
$begingroup$
Thanks! yes, I guess all recurring waveforms can be built up of sines, but this is a great answer as the phenomenon itself isn't really fundamentally like that (unlike, say, a body orbiting around another orbiting body)
$endgroup$
– topo morto
8 hours ago
$begingroup$
Thanks! yes, I guess all recurring waveforms can be built up of sines, but this is a great answer as the phenomenon itself isn't really fundamentally like that (unlike, say, a body orbiting around another orbiting body)
$endgroup$
– topo morto
8 hours ago
add a comment |
$begingroup$
However, I'm struggling to think of any other waveforms that can be
associated with phenomena in nature
This one has been getting some attention recently.
Image credit
answered 6 hours ago
Alfred CentauriAlfred Centauri
49.2k350155
$endgroup$
1
$begingroup$
That looks like a sinusoidal wave, though? It's just got its amplitude and frequency changing over time.
$endgroup$
– nick012000
5 mins ago
add a comment |
$begingroup$
However, I'm struggling to think of any other waveforms that can be
associated with phenomena in nature
This one has been getting some attention recently.
Image credit
answered 6 hours ago
Alfred CentauriAlfred Centauri
49.2k350155
$endgroup$
1
$begingroup$
That looks like a sinusoidal wave, though? It's just got its amplitude and frequency changing over time.
$endgroup$
– nick012000
5 mins ago
add a comment |
$begingroup$
However, I'm struggling to think of any other waveforms that can be
associated with phenomena in nature
This one has been getting some attention recently.
Image credit
answered 6 hours ago
Alfred CentauriAlfred Centauri
49.2k350155
$endgroup$
However, I'm struggling to think of any other waveforms that can be
associated with phenomena in nature
This one has been getting some attention recently.
Image credit
answered 6 hours ago
Alfred CentauriAlfred Centauri
49.2k350155
answered 6 hours ago
Alfred CentauriAlfred Centauri
49.2k350155
answered 6 hours ago
Alfred CentauriAlfred Centauri
49.2k350155
answered 6 hours ago
Alfred CentauriAlfred Centauri
49.2k350155
49.2k350155
1
$begingroup$
That looks like a sinusoidal wave, though? It's just got its amplitude and frequency changing over time.
$endgroup$
– nick012000
5 mins ago
add a comment |
1
$begingroup$
That looks like a sinusoidal wave, though? It's just got its amplitude and frequency changing over time.
$endgroup$
– nick012000
5 mins ago
1
1
$begingroup$
That looks like a sinusoidal wave, though? It's just got its amplitude and frequency changing over time.
$endgroup$
– nick012000
5 mins ago
$begingroup$
That looks like a sinusoidal wave, though? It's just got its amplitude and frequency changing over time.
$endgroup$
– nick012000
5 mins ago
add a comment |
$begingroup$
However, I'm struggling to think of any other waveforms that can be associated with phenomena in nature.
The motion of an ordinary pendulum of length $L$ is cyclic, but non-sinusoidal (it is only approximately sinusoidal for small angles). The exact non-sinusoidal motion is governed by the non-linear equation:
$$
fracd^2thetadt^2=-fracgLsin(theta)
$$
answered 8 hours ago
hfthft
4,1581922
$endgroup$
add a comment |
$begingroup$
However, I'm struggling to think of any other waveforms that can be associated with phenomena in nature.
The motion of an ordinary pendulum of length $L$ is cyclic, but non-sinusoidal (it is only approximately sinusoidal for small angles). The exact non-sinusoidal motion is governed by the non-linear equation:
$$
fracd^2thetadt^2=-fracgLsin(theta)
$$
answered 8 hours ago
hfthft
4,1581922
$endgroup$
add a comment |
$begingroup$
However, I'm struggling to think of any other waveforms that can be associated with phenomena in nature.
The motion of an ordinary pendulum of length $L$ is cyclic, but non-sinusoidal (it is only approximately sinusoidal for small angles). The exact non-sinusoidal motion is governed by the non-linear equation:
$$
fracd^2thetadt^2=-fracgLsin(theta)
$$
answered 8 hours ago
hfthft
4,1581922
$endgroup$
However, I'm struggling to think of any other waveforms that can be associated with phenomena in nature.
The motion of an ordinary pendulum of length $L$ is cyclic, but non-sinusoidal (it is only approximately sinusoidal for small angles). The exact non-sinusoidal motion is governed by the non-linear equation:
$$
fracd^2thetadt^2=-fracgLsin(theta)
$$
answered 8 hours ago
hfthft
4,1581922
answered 8 hours ago
hfthft
4,1581922
answered 8 hours ago
hfthft
4,1581922
answered 8 hours ago
hfthft
4,1581922
4,1581922
add a comment |
add a comment |
topo morto is a new contributor. Be nice, and check out our Code of Conduct.
topo morto is a new contributor. Be nice, and check out our Code of Conduct.
topo morto is a new contributor. Be nice, and check out our Code of Conduct.
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$begingroup$
The earth's orbit around the sun has had some attention from physicists.
$endgroup$
– WillO
8 hours ago
$begingroup$
Hardly anything is exactly sinusoidal. Picking nice functions for waveforms tends to be simply wanting an analytic solution, rather than that they are somehow realistic.
$endgroup$
– jacob1729
8 hours ago
$begingroup$
While we all love sin/cos and Fourier transforms, don't forget the various orthogonal polynomial bases out there, such as the Legendre, Tschebysheff, Jacobi, and Laguerre.
$endgroup$
– Jon Custer
8 hours ago
$begingroup$
@WillO in my naivety I'm seeing an orbit as effectively more or less a composition of sinusoids happening in more than one dimension at once... am I wrong to do so?
$endgroup$
– topo morto
8 hours ago
1
$begingroup$
Twisting words a bit: is it that nature always oscillates in sine waves, or is it that the thing you have chosen to define with the word "oscillate" is that which is described by sine waves, thus rejecting all natural motions which are not sine waves?
$endgroup$
– Cort Ammon
8 hours ago