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Offline Twenty8

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Sound wave arrival calculator?
« on: May 16, 2023, 08:46:00 AM »
Hypothetical.

Let's say I am running a pair of hypers PAS and a set of subcards NOS.

I want to figure out the difference in time between when sound (or a sound wave or sound waves) hit/s the hyper and the subcard.

Is there a calculator that does this?

Question out of curiosity rather than usefulness.  I am aware that not every wave that reaches the capsules are direct and that a large amount are reflected.  However I am curious if any one knows of and has used a calculator like this.
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Offline wforwumbo

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Re: Sound wave arrival calculator?
« Reply #1 on: May 17, 2023, 08:41:02 AM »
This depends on the angle of incidence of the capsule. For example, if you assume a plane wave and that both mics are aligned horizontally facing the stage, there is zero time delay. The corollary to that is if the angle of incidence is along the axis you have the mics mounted, you're at a theoretical maximum.

The average speed of sound in air at normal temperature and pressure (approx. 68 degrees and 1 atmosphere) is 343 meters per second. To find the amount of time it takes for a sound wave to travel a given distance in meters, take the distance and divide it by 343 - in this thought experiment, for sound to travel 1 meter it takes (1 [m] / 343 [m/s]) or approximately 3 milliseconds. If we take ORTF microphones, we would do (0.17 / 343) which is approximately half a millisecond, which would be traveling along the long axis the mics are mounted on.

To take into account the angle of incidence, multiply this number by the cosine of the angle from the axis the mics are mounted on. So if your mics are in ORTF and oriented at a 45 degree angle to the stage, there is a 0.35 millisecond time delay between the plane wave reaching your two microphones.

Caveat emptor that this assumes a plane wave traveling to both your microphones. It gets more complicated when you take into account the angle/orientation of two PAs and the angle of the mics oriented to both of them.
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Online Gutbucket

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Re: Sound wave arrival calculator?
« Reply #2 on: May 17, 2023, 12:29:50 PM »
I'm not aware of an online calculator that does this for you, although one could certainly be produced or may be available.  I did check http://www.sengpielaudio.com/ which features a lot of other useful audio and acoustic calculators, but unfortunatley not this.


To clarify a bit on the geometry aspects, in addition to the math required to get the actual solution which wforwumbo sums up nicely above-

The direction in which each individual microphone of a stereo pair is pointed will have no influence.  What does are two things: 1) The angular difference between the wavefront arrival of the sound in question and the axis along which the microphones are spaced, and 2) How far apart they are spaced.

Wavefronts arriving along the medial plane (from directly in front, directly behind, above, below..) will produce no time of arrival difference between channels, whereas wavefronts arriving from fully 90-degrees off to one side or the other will produce a maximum time-of-arrival difference between channels, determined by how far apart the spacing is.  Wavefronts arriving somewhere between those two extremes will produce time-of-arrival differences that are dependent on and change with the angle of arrival.  This is where the cosign function comes in.

All of the above is true in regards to time-of-arrival differences between a single stereo pair of two microphones.  With two pairs it will also matter if both pairs share the same spacing axis or not, and their positions relative to each other.


In your case, lets assume the to pairs share the same spacing axis and are symmetrically arranged with respect to each other. If the spacing between the PAS hyper pair and the subcard NOS pair happens to be identical (PAS pair mounted directly above or below the NOS pair), the time of arrival differences will be identical for both pairs.  Both pairs will produce no time difference between channels for wavefronts arriving from directly ahead.  Both will produce increased timing differences the farther the source is off center. And the timing differences produced by the two pairs for off center sources will be the same. If instead the PAS pair is spaced differently than NOS, there will still be no difference in time-of-arrival between the two pairs for any wavefronts arriving along the median plane, and as before, in each pair arrivals from further and further off the median plane will create increasing time-of-arrival differences.  But in addition, the time-of-arrival differences between the two pairs will grow increasingly different as the wavefront arrival moves increasingly farther and farther off center. 

Lots more complexity generated by two pairs that are spaced differently.
« Last Edit: May 17, 2023, 12:32:14 PM by Gutbucket »
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Re: Sound wave arrival calculator?
« Reply #3 on: May 17, 2023, 12:42:44 PM »
I am aware that not every wave that reaches the capsules are direct and that a large amount are reflected.

These time-of-arrival differences between channels are relevant to distinct wavefronts travelling directly from a source to the microphones - the earliest 1st arrival of any discrete sound traveling along a straight line-of-sight from the PA, stage sources, specific audience members, discrete reflections, etc. 

The diffuse reverberant component of the sound effectively arrives in equal amounts from all directions.  With a spaced microphone pair it won't have one specific time-off-arrival onset between the two channels.  Instead the specific onset time is going to differ slightly across all possible angles of arrival, spread out somewhat over time.  With two paced pairs, that complexity becomes even more densely complex.

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Offline wforwumbo

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Re: Sound wave arrival calculator?
« Reply #4 on: May 17, 2023, 01:45:28 PM »
I am aware that not every wave that reaches the capsules are direct and that a large amount are reflected.

These time-of-arrival differences between channels are relevant to distinct wavefronts travelling directly from a source to the microphones - the earliest 1st arrival of any discrete sound traveling along a straight line-of-sight from the PA, stage sources, specific audience members, discrete reflections, etc. 

The diffuse reverberant component of the sound effectively arrives in equal amounts from all directions.  With a spaced microphone pair it won't have one specific time-off-arrival onset between the two channels.  Instead the specific onset time is going to differ slightly across all possible angles of arrival, spread out somewhat over time.  With two paced pairs, that complexity becomes even more densely complex.

Funny enough, the two spaced pairs in a purely diffuse field is actually an easy problem to solve - the mixture of the two Gaussian functions is another Gaussian function. So, the time delay between microphones is still purely stochastic, just with a different mean and variance that are a function of the distance between the two caps. Looking at any mixture of free and diffuse responses across two (or more) spaced pairs is actually significantly more complex than the purely free or diffuse cases.
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Re: Sound wave arrival calculator?
« Reply #5 on: May 17, 2023, 03:01:20 PM »
Thanks for the mathematic description and terms!

"Looking at any mixture of free and diffuse responses across two (or more) spaced pairs is actually significantly more complex than the purely free or diffuse cases." 


Sounds to me like a good description of taping in general, and the combination of taper microphone pairs in particular.


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Offline morst

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Re: Sound wave arrival calculator?
« Reply #6 on: May 26, 2023, 03:31:33 AM »

Physics ahoy!


Popcorn anyone?? :drool:


(I am following this thread! Been busy at work lately, but color me fascinated!)
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Offline jielkade

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Re: Sound wave arrival calculator?
« Reply #7 on: May 26, 2023, 05:03:33 AM »

 

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