more added to o.t
Reflections and Room Modes
Room modes are the core of the acoustics and acoustic treatment of confined spaces. Think of a room like a music box, or a sound box of a guitar or a piano. A room is hollow and filled with air. Perfect environment for resonant behavior. It is true that each room is like a musical instrument with hidden resonant frequencies that live within.
I tried to keep it as simple as possible to explain this phenomenon without going into too much nerdy details like nodes and anti-nodes, trying a basic mathematical approach to explain.
(however, requires a bit of knowledge of basic geometry)
It is no secret that sound can bounce of walls, ceilings and structures. These are called reflections. Although they are not exactly reflections like light rays off a mirror but When we are dealing with sounds in the human
hearing range inside a room where wavelengths are somewhat around or within the boundaries of the room- we can treat their behavior like light rays (this is a whole another topic)
If we treat them like rays, we can then use geometry to analyze the reflections in basic cases. When a sound wave is reflected back from a wall or combination of walls - at a certain wavelength of sound they will exactly combine (superimpose) on top of each other to deliver a standing wave. Its called a standing wave because when 2 waves traveling in opposite directions meet, they come to a halt as in appear to stand still but still transfer energy back and forth.
These standing waves are static frequencies and their multiples that resonate inside a room are called “Room Modes”
Room modes are internal resonance of a room that exist when you turn on your loudspeakers. These are, static frequency hums inside that get stronger when a particular frequency or multiple of that frequency is played.
Lets say sound reflected back and forth between two parallel walls (axial mode)
If the room is 10 feet long, the round trip of sound back and forth is 20ft.
A sound with 20 feet wavelength will fit snug like a condom within that length, holding a nice load of standing wave at that frequency.
Now what sound has a wavelength of 20 feet? lets find out
1130/20 = 57 Hz (reminder: 1130 is the speed of sound)
this means when you excite the room with sound around 57hz, the room will start moaning and groaning around that frequency and multiples of that frequency (harmonics). Room modes can exist from 20 hz upto 300hz in complex cases. After that they still exist but they are somewhat of a less problem.
There are 3 types of room modes
The one we discussed above is axial between 2 parallel walls, it is the simplest of the cases and a 6th grader should be able to calculate those.
In tangent mode, sound bounces around the 4 walls instead of 2. These are less intense than those with 2 walls back and forth. Normally around half as strong as axial modes of the same room. (how? is a discussion for another time)
In lets say a room, if sound bounces off 4 walls it would generate a standing wave with a wavelength equal to the length of the diagonal of the room in its basic case. (Thank you Pythagoras)
In a basic case, in a 9 by 12 room, sound will bank tangentially, forming a standing wave of wavelength 15 ft (Note: 9,12 and 15 are Pythagorean triples). So the resonant frequency of tangential mode would be around a wavelength of a wave that fits snug in 15 feet is 1130/15 = 75 Hz (approximately)
75 hz and its multiples is one of the resonant frequencies for a Tangential room mode of a 9x12 room.
This time sound bounces around 6 walls (4 walls and ceiling and floor)
This is the weakest of the 3 modes and less problematic. This case of a reflection is a bit more complex to compute geometrically because pressure at more oblique angles is a lot less than the other 2 cases, but in one of the basic cases sound will approximately form a standing wave at a fraction (around inverse of square root of 2, roughly about two thirds) of the distance of the “large diagonal” (for example, the distance between top left and bottom right corners of the room in its basic case)
- Mr Pythagoras visits again <-
If your room is 10 feet by 12 feet by 8 feet tall, the large diagonal will be about 17 feet.
Sound will form one of the standing waves at around roughly two thirds of it as wavelength, so about 11 feet . The frequency at 11 feet is 1130/11 = 102Hz (approximately)
102 hz and its multiples will become the resonant frequency of the room in oblique mode.
Ofcourse as we think of other ways sound can reflect, there are many ways it can bounce of the 6 walls. Geometry gets extremely complicated. while, using geometry we can approximate for basic scenarios but they get complicated as we progress further and a more pressure driven approach is needed.
Using calculus ( partial differential equations) we can use a pressure or molecular displacement driven wave equation to calculate resonant frequencies in confined spaces easily. After years of caffeine driven calculus you will arrive at an equation we can all easily use. Thankfully some crazy dude Rayleigh did it for us so we never have to.
Rayleigh Room mode equation:
The above equation is a bit more accurate than the traditional geometry methods, while both methods will yield results around the same frequencies.
Lx, Ly, Lz are room dimensions -
Lx = Length
Ly = Breadth! @FluteCafe
l, m and n are integers normally within (0 to 4) that help calculate different room modes
l, m and n correspond to axes x, y and z respectively.
For basic cases:
axial use [
l = 1 , m=0, n=0 ] or [
l=0, m=1, n=0 ] or [
l =0, m=0,n=1 ]
tangential use [
l = 1 , m=1, n=0 ] or [
l=0, m=1, n=1 ] or [
l =1, m=0,n=1 ]
oblique use [
l = 1 , m=1, n=1 ]
v is speed of sound 1130 ft/sec , result will be in Hz.
If someone is interested in how this formula is derived, I can shed more lights on the calculus and wave equations involved if you pay for coffee .
Thats all for now, will shed more light on importance of geometry of a room.
Next up, more on reflections, diffusion, materials and importance of geometry of the room
Anyway, that is all for now folks… will add more to it as time permits.