What does sin(1/X) sound like?

[Chiwalker]

So a sin wave sounds like doooooooooooooo

Say you can listen to what the sound wave sounds like from -10pi to 10pi

As it got from -10pi to 0, it would start increasing in pitch (because of an increase in frequency of oscillation), from 0 to 10pi would decrease in pitch.

So what would it sound like when you got to 0 (where it is infinitely oscillating)?

Better question - would it ever get from - to + ?

[Bleck]

the brown note basically

[Antipode]

Is there a program where you can enter an expression and listen to the resulting wave?

[Gollgagh]

tan(x) would blow out your speakers

actually probably not

it'd probably sound like "woop woop woop woop"

[Moseph]

So what would it sound like when you got to 0 (where it is infinitely oscillating)?

Wouldn't sound like anything. Once the sine wave exceeded 20kHz we wouldn't be able to hear it.

Better question - would it ever get from - to + ?

As long your software or whatever won't crash on a divide-by-zero error, the x = 0 point shouldn't cause problems. As you said, approaching x = 0, the pitch would rise until you couldn't hear it. Once past x = 0, it would come back down until it was it was too low to hear.

[Antipode]

woop woop woop woop

[Sengin]

So what would it sound like when you got to 0 (where it is infinitely oscillating)?

Better question - would it ever get from - to + ?

Well, since the human ear on average can't detect pitches greater than 20KHz or so, a person couldn't hear it.

As for your second question, ...possibly. Before you get to a point in time one second from now, you must get to a point in time 0.5 seconds from then. But before that, you must get to a point in time 0.25 seconds from then, etc... If you think about it like that, then yes, it would get to the positives. However, if you think about it a bit differently in that it's not based on time elapsed, then no, it would not get to the positives, or even to 0 for that matter.

But since it would be digitally replicated, it wouldn't be at an infinite resolution (that would be analog), and since speakers have a maximun frequency they can output, it would just sound really low pitched for a whlie, get higher, then sound really high pitched for a short while, disappear out of your hearing range for a brief moment, have a really high pitch getting lower and lower.

Edit: Wow, 5 posts as I was typing mine.

[Chiwalker]

Well, since the human ear on average can't detect pitches greater than 20KHz or so, a person couldn't hear it.

Ok, but what effect on us does happen at a frequency greater than 20KHz?

I actually don't know why we can't hear that high - is it because the hair cells are too thick to pick up vibrations that fast?

Anyway, it seems as if something bad would happen if we were in the presence of a frequency of ∞ Hz, right? Finding a speaker that can propel such high frequencies would be the first step...

[Nohbody]

I wonder what sinh(x) would sound like?

[Chiwalker]

I wonder what sinh(x) would sound like?

If you mean sin(x) (what's the h for?) then it is just steady constant tone, no change in pitch.

[Gollgagh]

I wonder what sinh(x) would sound like?

If you mean sin(x) (what's the h for?) then it is just steady constant tone, no change in pitch.

http://en.wikipedia.org/wiki/Hyperbolic_trigonometric_function

yeah, I'm pretty sure a hyperbolic function wouldn't even sound like anything

[Nohbody]

If you mean sin(x) (what's the h for?) then it is just steady constant tone, no change in pitch.

sinh means hyperbolic sine. Instead of the unit circle, sinh values correspond to values on a unit hyperbola. the value of sinh(x) = (e^x - e^-6)/2. Which would make for a very odd sounding tone, if any.

EDIT: damn golagh why so lazy? i remember the days when there was not a webpage for every concept ever concievable.

[Gollgagh]

I'm doing other things at the same time that require more attention than explaining functions to some dude over the internet.

[Chiwalker]

ok, but the problem is sinh(x) isn't a wave, so it wouldn't work in this case

[q-pa]

actually probably not

it'd probably sound like "woop woop woop woop"

woop woop woop woop

But that's the sound of da police!!

[Effef]

woop woop woop woop

woop woop woop woop woop

[dish]

Heheh, interesting topic

Ok, but what effect on us does happen at a frequency greater than 20KHz?

I actually don't know why we can't hear that high - is it because the hair cells are too thick to pick up vibrations that fast?

Anyway, it seems as if something bad would happen if we were in the presence of a frequency of ∞ Hz, right? Finding a speaker that can propel such high frequencies would be the first step...

The range of frequency we can hear is decided by the cochlea. My understanding is that different part along the cochlea reacts to different frequency; and it happens that the whole length covers the frequency from 20 Hz to 20 KHz. I guess we can hear frequencies beyond 20 KHz if we can "extend" the cochlea (though that part is likely to be damaged quickly because of the fast fibration).

Wikipedia reference: http://en.wikipedia.org/wiki/Cochlea#Function

I'm not sure about ∞ Hz frequency. Doesn't that involve relativity since the vibrating object has to travel infinite distance in 0 s (faster than light)? I think it will feel hot because the friction within air particles that transfer the wave...

[Chiwalker]

Well, since the function contains division by 0 (if x = 0) then it would be moving air so fast that it would maybe tear a hole in the fabric of space and a black hole would be created...

[Antipode]

woop woop woop woop

woop woop woop woop woop

woop woop woop woop woop woop

[Sengin]

Well, since the function contains division by 0 (if x = 0) then it would be moving air so fast that it would maybe tear a hole in the fabric of space and a black hole would be created...

In the same respect, it could just disappear, move out of the 3 dimensions we live in, or do something we haven't even thought of. Since the action of dividing by 0 is undefined, perhaps what happens is undefined. If it's undefined, then there is absolutely no possibility of it happening, so there's no need to try and find out what would happen. Or, our mathematical system could be missing a key concept that allows things that are currently undefined to occur. In that case, then we really don't know what would happen.

At the question of hearing tones >20KHz: I don't really know. I assume that tones near 20KHz we just wouldn't hear and wouldn't cause damage, but at some point, I imagine that it would hurt, but you still wouldn't be able to hear it. I assume that a 20Hz tone and a 20KHz tone at the same volume have different energies. Because the 20KHz has to vibrate a lot faster in the same amount of time, it has more energy. What would happen if it were a 1MHz tone (1,000KHz)? The energy there would be massive, and my guess is that it would screw up part of your ear/inner ear (cochlea, etc...), and brain, at the least.

Hmm...if something traveled an infinite distance in 0 seconds, wouldn't that mean that it's omnipresent and is everywhere at the same time? Kinda like static? But what happens at the 13 billion or so light years away from Earth at the end of the universe? Warp around to the other side? Change dimensions? Random worm hole? Ceases existence?

[Sinewav]

I heard people were talking about me in this thread.

[SLyGeN]

In order to hear a sound, you need to be living in the fourth dimension, time. These trig functions aren't usually graphed with any respect to time.

Now, if you saw a graph like this on a sound editor and played it back, it would sound like a high "BEEEE", and move down to a low "ooooh". Since you haven't specified a time (playback, like 1 unit per second) variable, then I'll also add that as your playback variable increases, each increment of time will sound higher pitched and vise versa.

I'm not sure about your concepts of infinity, though. That would be limited by a sample rate.

Also, you guys talking about ultrasound waves, any of you working on a wireless router are having 2,400,000KHz waves sent through your body every day. (That's 2.4GHz.. sound familiar?)

Correct me if I'm wrong on any of this info.

edit: I was lazy and looked up the graph, and it turns out it only showed an interval from 0 to.. .. something. So my explaination is based on that. You have to specify a starting point. So if you start negative, it'll sound like BEEEeeeoooooeeeEEEEE....

[Bundeslang]

I really want to hear something like:

(sin(e^x) * d)/(cos(3 nCr 5 * pi) (For all d > 0, cos(3 nCr 5 * pi not equal to zero)

I know there are infinite possibilities (since d could be any value above 0).

[Drack]

Assuming you start at x=0, sin(1/x) would start at a very high pitch and quickly descend to a very low pitch.

It wouldn't be very interesting, to be honest.

[Sengin]

Also, you guys talking about ultrasound waves, any of you working on a wireless router are having 2,400,000KHz waves sent through your body every day. (That's 2.4GHz.. sound familiar?)

Correct me if I'm wrong on any of this info.

Routers don't use sound waves as their choice of communication. Light and sound are different types of waves. Light waves are radio/micro/IR/visible/UV/XRay/Gamma/Cosmic waves, and are used everywhere from routers, phones, radios, medical equipment, etc. These are transverse waves. Sound waves, on the other hand, are longitudinal waves, which are caused by anything moving, which cause the molecules in the air to compress and rarefact. These waves have different properties (like actually moving the air around it). The different types of waves are why you need eyes AND ears, and why you can't "hear" light or "see" sound (synthesia is a bit different, I mean how your eyes do not pick up and translate sound waves into something your brain can understand - that's what your ear is for, and vice versa with your ears and light waves).