I know a sine wave is a linear representation of a circle, and sound can be broken down into sine waves. Are sound waves in the physical world (rather than analog) circular?

Thanks

Sound moves in all directions, so it's spherical. Drop a pebble in a still body of water. That's how sound waves move.

In air, the particles aren't physically moving up and down like a sine wave. Think of the sine wave as a representation of air pressure, and then after the transducer, voltage (higher air pressure is transduced into higher voltage). If you've ever made waves with a slinky, you can either move the end side to side in relation to the length of the slinky, which is called a transverse wave, or in and out, which is called longitudinal. Sound waves in air are more analogous to the latter.


where you see the wave in the slinky is where the coils are compacted, and the other points are where it is rarefied. It is the same in air.

Sound Waves? HELL YEAH!

haha I'm in love with sound waves =)

the missing bit here is "on a complex plane" - it's a circle with real and imaginary components, a mathematical fiddle which helps you to do sums.
A sine wave is the REAL component of this imaginary circle as the phase angle changes.

You could represent a waveform as the real part of the vector sum of all the imaginary circles (representing the partials of the wave) in the complex plane I suppose.

However, I think you are confusing the mathematical and physical worlds.

I the real world, sound waves can be spherical, cylindrical or plane depending on the type of source and how close to that source you are.

K.

It is a long time since I was at university, but I’m sure that the mathematical representation for a sine wave isn’t complex.

A complex number takes the form (at its most basic) of a + bi, where a and b are real numbers and i is imaginary (square root of -1) which makes the bi part of the above expression imaginary.

From Wikipedia the expression for a sine wave is:



I don’t see any imaginary part to this expression.

Omega, the angular frequency, can be represented by a radius rotating round a circle, and as it is varying in time the resultant graph is the characteristic sine wave.



If you imagine the sine wave to be moving forward, the diagram represents a transvers wave. This is because the particle velocity is perpendicular to the motion of the wave (up and down). Neither gasses nor liquids can sustain the transverse shear necessary for transverse waves, hence sound waves are longitudinal. Solids can sustain both transverse and longitudinal waves so propagation can be more complicated.



The Fourier transform enables signals to be transformed between the time and frequency domains. A complex (non sinusoidal) signal, such as you might see on an oscilloscope or DAW track, which is varying in time, can be transformed into the frequency domain where each time slice can be represented by a number of sine waves. The transform can work both ways.

Some audio analysers use a fast Fourier transform to display the frequency response of a time varying signal coming from a device under test. The fast bit just means that the device uses some algorithm to speed up the calculations. A single channel FFT device would give what is usually referred to as a RTA. To obtain a transfer function (comparing two sources usually input and output) a dual channel FFT is needed.

Sound waves are pressure variations in matter (air - usually). If you can remove matter (e.g. a vacuum) then there are no sound waves. And it takes energy to move particles around, so friction comes into play. This is why high frequencies die off faster than low frequencies - which is why you hear the thump long before you hear the sizzle when you approach a party.

Loud speakers have various dispersion patterns - so it is not true to say that all sound waves travel in a perfect sphere from the sound source. Perhaps a special pulsating globe speaker could be produced that literally does have a true omni-directional spherical dispersion pattern - but I haven't seen one.

Having said that - pressure equalizes in a fluid and attempts to find equilibrium. I guess this is why bass tends to be omni directional, and highs are much more directional. Because there is more time for the low speed bass waves to equalise and disperse the pressure.

If we could see complex waveform in a fluid, it would be much clearer how complex they are. I think you can find experiments of waves in water, and very complex geometric patterns can be created by varying the frequency. Not sure if crop circles are done this way, but there are some complex geometric patterns in some of the planets that appear to be the result of waveform interactions.

When a sound wave is said to be radiating spherically it does not necessarily mean that it is radiating as a complete sphere.

A loudspeaker converts electrical energy into sound energy and heat. Close to the loudspeaker the power is concentrated into a small area so the power density is high. As the energy radiates out it is spread out over a bigger area and the sound density gets less.

When a sound source is radiating spherically it means that the area which the sound radiates through increases proportionally to the square of distance from the source. Doubling the distance increases the area by a factor of 4 so the sound density decreases by 4 and the sound level goes down by 6dB.