Sound waves on the Sun

[sevensages]

TL;DR

Tegmark wrote "A sound wave on the Sun will cancel itself out with destructive interference unless it performs exactly a whole number of oscillations as it goes around". What the heck does a whole number of oscillations mean?

I am reading Max Tegmark's book Our Mathematical Universe. On page 172, Tegmark wrote the following: "Two waves can pass through each other unaffected, like the circular waves in the water tank in Figure 7.6; at any time, their effects simply add together. In some places, we see peaks of the two waves adding up to an even higher peak (so-called constructive interference), in other we see a peak from one wave cancelling a trough from the other to leave the water completely undisturbed (so-called destructive interference). On the surface of the Sun (Figure 7.6 center), sound waves in the hot gas/plasma have been observed. If such a wave propagates all the way around the Sun, then it will cancel itself out with destructive interference unless it performs exactly a whole number of oscillations as it goes around, thereby staying in sync with itself. This means that, just as a flute, the Sun vibrates only with certain special frequencies."

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This thread is about what Tegmark wrote that i wrote in green font above.

The meaning of Tegmark's quote seems to me to depend on the meaning of the word whole. Normally, I think that the word whole is roughly synonymous with the word "entire", but that meaning does not make much sense to me in this context.

Is Tegmark saying that the sound waves on the Sun will cancel themselves out with destructive interference unless the Sound waves stay just as strong through the sound waves' entire trip around the circumference of the Sun? If not, what does Tegmark mean? I am confused.

 

[berkeman]

What the heck does a whole number of oscillations mean?

What part of $N * 2\pi$ do you not understand?

 

[sevensages]

What part of $N * 2\pi$ do you not understand?

I don't know what N*2pie equals. And I don't know what the N in N*2Pie stands for. I have no clue why you mentioned N*2Pie. I had never even heard of N*2Pie in my life before you made that post a few minutes ago.

 

[sevensages]

@PeterDonis

You are good at explaining complex things to a layman. Please help

 

[sevensages]

What part of $N * 2\pi$ do you not understand?

I am not a physicist or an engineer like you probably are. I am a long distance truck driver. I need you to explain it to me like I am a five year old

 

[berkeman]

I am not a physicist or an engineer like you probably are. I am a long distance truck driver. I need you to explain it to me like I am a five year old

So for sine waves to build while cycling around something, they need to be in-phase. A sine wave is 360 degrees total in length, or $2\pi$ radians in length. So for the sound waves traveling around the Sun to add and not cancel out, they need to be in phase, hence some number N of $2\pi$ wavelengths:

https://en.wikipedia.org/wiki/Standing_wave

 

[Ibix]

Here's an orange circle with a green wave:

In places the green wave is outside the orange circle, in places it's inside. You can think of the orange circle as an undisturbed sun and the green shape as the sun with a (very low frequency) sound wave disturbing it. (Do note that sound waves are longitudinal and I've drawn a transverse wave, but longitudinal waves are really hard to sketch. So this isn't quite accurate, but the important features are here.)

Notice that there are six complete waves in the diagram. This is the kind of wave Tegmark is describing as "a whole number of oscillations as it goes around".

Now here's a version of the diagram where the wave doesn't do a whole number of oscillations:

This time, I've picked a wavelength that doesn't evenly divide the circumference of the circle, so it doesn't meet itself. In terms of a wave, that means that if it wraps round the sun it is both trying to push the surface up and push it down at any one place. Averaged over a few laps, the "up" and "down" motions cancel each other out and the wave dies out rather than reinforcing itself.

I have to say that I'm not sure Tegmark is helping here. What he is describing is actually something quite familiar, but in an unfamiliar setting and in a rather abstract way. You know you can tap a bell and it rings, and different size bells ring with different tones because bells resonate at particular frequencies, right? It turns out to be true of anything that's free to move, like wine glasses and bowls, but also the earth and the sun. That's what he's describing - the Sun vibrating like a bell at its resonant frequency (although in this case, driven by its own internal energy sources rather than Thor passing by with his hammer).

It turns out that the resonant frequency of a sphere is related to the frequency of sound waves whose wavelengths exactly divide the circumference of the object - because other wavelengths cancel themselves out quickly as they wrap around (as in my second diagram). It also turns out that any disturbance of the surface can be split up (mathematically, anyway) into a little bit of the wave that fits once plus a little bit of the wave that fits around twice plus a little bit of the wave that wraps around three times plus... Taking advantage of this fact applied to normal sound waves (instead of waves on spheres) is how spectrum equalizers on fancy hi-fi systems work - they split out the low, middle, and high frequencies making up a single sound and let you amplify them (or not) separately before recombining them with stronger bass or whatever.