Critical Frequency and Coincidence?

Can someone explain "critical frequency" and "coincidence" to me? I'm specifically reading the section on glass in Rod's book, and the only other reference I can find is on page 36 - which says the following:

For every frequency above a certain critical frequency, there is an angle of incidence for which the wavelength of a bending wave can become equal to the wavelength of an impacting sound

Is this related to resonant frequency? or standing waves at all? Thanks, Todd

I will try to translate what I know to english. I hope to use the correct technical words. There is a natural frequency or resonant frequency, which is the frequency that material vibrates (like a drum), normally in low frequencies. There is also a critical frequency, which appears when the material is vibrating, because there are flexion waves along it. The coincidence frequency is when the incidence wave coincides with the critical frequency. hope it helps edited: I made a mistake explaining the coincidence effect

Thanks for the info! So... I think I'm beginning to understand. When a material or structure (such as a wall, or a piece of glass) is vibrating because(?) of a it's resonant frequency - it then vibrates AT it's critical frequency? Is that close? What are "flexion waves"? Can/would critical and resonant frequency be different frequencies? If so - why? Wouldn't the frequency that a material vibrates sympathetically at - be the same frequency it produces when vibrating sympathetically? Is it related to harmonics? Thanks! Todd

gbondo9 wrote:

When a material or structure (such as a wall, or a piece of glass) is vibrating because(?) of a it's resonant frequency - it then vibrates AT it's critical frequency? Is that close?

Yes, it should be a vibration which appears due to the natural vibration

gbondo9 wrote:

What are "flexion waves"?

Hmm... longitudinal waves, along the material

gbondo9 wrote:

Can/would critical and resonant frequency be different frequencies? If so - why?

They are different. Because? I don't know, they just exist by different reasons.

gbondo9 wrote:

Wouldn't the frequency that a material vibrates sympathetically at - be the same frequency it produces when vibrating sympathetically? Is it related to harmonics?

I don't understand your last question, sorry. Anyway I'm not expert in the theme, you maybe should pick a book on vibroacoustics or maybe somebody in the forum could clarify more these things. Haven't you ever seen a tipical wall behaviour graphic? I'll try to find you one.

Resonance and coincidence are not the same thing. Resonant frequency (fr) is dependent on the dimensions of the panel, as well as other mechanical properties such as bending stiffness and surface density. For many building materials, the lowest fr typically occurs at frequencies too low to be of concern. Above fr, up to fc (see below), transmission loss (TL) in a panel is mostly governed by the mass of the material and a ~6 dB per octave TL is typically observed. Below fr, TL is controlled by the stiffness of the panel. Examples: fr for 3 m x 3 m concrete wall, ~200 mm thick = ~71 Hz. fr for 5 m x 5 m concrete floor, ~200 mm thick = ~26 Hz. fr for 1 m x 1 m glass window, ~3 mm thick = ~6 Hz. Coincidence occurs when the wavelength of the bending wave in the panel coincides with the wavelength of sound in air. At this frequency (fc) a "dip" is experienced in TL as vibrations in the panel sympathetically reinforce the airborne sound. The reduction in TL is also apparent above fc, but the mass law "kicks back in", albeit at a reduced overall TL due to the effects of coincidence. The fc is controlled by, again, surface density and bending stiffness, but also by the speed of sound - and not by panel dimensions. How much coincidence affects TL depends on energy losses in the material, or to other parts of the structure. In general, relatively smooth dips are experienced for materials like concrete, whereas the dip can be very sharp for materials like glass. To that end, the most obvious real-world experience of coincidence can be observed directly when it is raining outside. The frequency range of the sound of tires on a wet road overlaps quite well with fc of many types of window glass. Thus, the high frequency "whoosh" that seems easier to hear when cars pass by your windows on a rainy day. (Easier, that is, relative to a dry day.) Examples: fc for 200 mm thick concrete wall = ~92 Hz. fc for 3 mm glass = ~5100 Hz.

References: Noise Control for Engineers by Lord, Gatley, & Evensen Handbook of Acoustical Measurements and Noise Control, ed. by Cyril M. Harris. Note that the examples above are calculated for specific materials; assumptions not relevant to the explanations have been omitted. They do not represent universal values to be used in design. The composition of materials like glass and concrete vary widely around the world. Thus, YMMV. :)

HTH. All the best,

I have found this link with that behaviour graphic and a good explanation about all this. http://www.kemt.fei.tuke.sk/Predmety/KE ... ssion.html There is also a good image explaning the coincidence effect in the F. Alton Everest book (Sound Studio Construction) in page 174.

Thanks lovecow, that's a better explanation :D

No problem. Put more simply, resonance is a property of the panel itself. If a piece of machinery mounted on a concrete slab vibrates at the fr of the slab, resonance will occur. Coincidence assumes the presence of airborne sound incident on the panel. A piece of machinery mounted on a concrete slab vibrating at the fc of the slab will not induce coincidence effects since the incident energy is not airborne. (Of course, any airborne sound emitted by the machinery at fc will result in coincidence effects as the airborne sound passes through the slab.)

lovecow wrote:

Of course, any airborne sound emitted by the machinery at fc will result in coincidence effects as the airborne sound passes through the slab

Yes, fc and above! (for the angle of incidence issue) I found a graphic very similar to the Alton Everest one: Obviously it will be more difficult to put it into vibration as the frequency increases because the angle has to be greater, but it's possible.

This is awesome (as usual)!! Thank you!

OK - couple more questions: The "bending wave" that is occurring along the panel itself - is that a different frequency that the resonant frequency(s)? Or is the same? In the diagram - It appears that the bending wavelength is longer (and thus the frequency is lower) than the incident sound wavelength. Is that accurate? The "Critical Frequency" range is referring to the incident sound waves - and not the bending wave? Correct?

gbondo9 wrote:

OK - so 1 more question: The "bending wave" that is occurring along the panel itself - is that a different frequency that the resonant frequency(s)? Or is the same?

Bending waves occur at all frequencies. They are not resonances. When the wavelengths of airborne sound waves match those of the bending waves, they coincide as shown above.

In the diagram - It appears that the bending wavelength is longer (and thus the frequency is lower) than the incident sound wavelength. Is that accurate?

(That's two questions. :) ) That's because the speed of sound (c) in the panel is different than c in air. Coincidence is dependent on angle of incidence, as shown. E.g., a wavelength that is coincident at X° will not be coincident at Y°, X ≠ Y or Y + (or -) 90°. The coincidence dip occurs where things really start to line up well between air and the panel medium. Coincidence occurs at and above fc.

The "Critical Frequency" range is referring to the incident sound waves - and not the bending wave? Correct?

(Three. :) :) ) Both. Airborne sound waves and panel bending waves are coincident in terms of wavelength at certain angles of incidence. This affects TL at and above fc.

I apologize if I'm starting to repeat my questions - but I really want to understand this, and for some reason - it's just not clicking 100% yet. Can you give me a definition for "Bending waves". You said they happen at all frequencies - and that confuses me. :oops: What I think I got from the posts in this thread so far is this (please correct this is any of it's incorrect): When sound that is traveling through a panel (as a bending wave?), and sound that is traveling through the air coincide at a specific angle (the angle of incident) on the panel - they will pass through the panel easier than normal. This happens at the critical frequency and above (although it lessens at it rises). The critical frequency for a panel is determined by the physical properties of the panel itself. I want to understand the conditions that bring this about. If the resonant frequency doesn't have anything (specifically) to do with the occurrence of a bending wave on (in?) a panel - then what does?

"Bending waves" is just a fancy way of saying "sound waves in the panel in a longitudinal direction." All sound waves pass through a solid material just like all sound waves pass through a gaseous medium such as air. When sound travels through a solid panel, sound travels longitudinally as bending waves, as shown in the above illustration. Because the speed of sound in the solid is different from that of air, coincidence can only occur when the wavelengths coincide at certain angles of incidence for the airborne sound wave.

Jeff, I know you know but to prevent confusion. The waves travels in a longitudinal direction of the panel but is a mainly traverse wave unlike a wave in air which is longitudinal.

Eric, Yes. :)