Room acoustics (Version of 09.07.1999)

Especially in the low frequency range the impression at the listening location is influence very much by room reflections.
In each room with parallel walls so called 'standing waves' occur at those frequencies where the sound wave length fits 'good' between the parallel walls.

The wavelength Lambda is:

Lambda = c/f
with
c - speed of sound in air, approx. 340 m/s at 20°C
f - frequency in Hz

Solved for frequency this becomes:

f = c/Lambda

If the distance between the parallel walls is a multiply of half the wavelength then the wavelength fits 'good' and 'standing waves' (a local increase of sound pressure) will occur. The frequency where this happens is called resonance frequency or room mode.
For a room dimension of 5.00 m standing waves will occur at frequencies with wave lengths of 10.00 m, 5.00 m, 3.33 m, 2.50 m, 2.00 m etc., that means for frequencies of 34.0 Hz, 68.0 Hz, 102.0 Hz, 136.0 Hz, 170.0 Hz etc..

A standing wave can be excited ideally if the noise source is located directly beneath the wall or in a distance of x*Lambda/2 from the wall responsible for the standing wave.
In a distance of (x+0.5)*Lambda/2 from the wall a standing wave can not be excited.

An excited standing wave is found to be annoying only if the listener is located as well at a place with increased sound pressure thus directly beneath a wall responsible for the standing wave or in a distance of x*Lambda/2 from the wall.
If the listener is located in a distance of (x+0.5)*Lambda/2 from the wall an excited standing wave can not be detected.

A balanced impression can be achieved if the excitation and response is located around (x+0.5)*Lambda/4 ('excite normal' and 'hear normal').

For this problem a simple graphical solution exists:

1. Draw a scaled sketch of the room (starting with length and width).
2. Redraw the wall with a wide pen. This should remind you that standing waves can be excited very good at these places.
3. Initially the room length will be halved. This line has to be redrawn again with a wide pen (you're right: also at these places a standing wave can be excited very good, but with doubled frequency).
4. Next the room length is divided into 3, 4, 5 etc. parts until the distance between any of these lines is less than 30 cm. Please redraw the lines again with a wide pen.
5. Please perform the same for the room width. Your sketch will now look like a mesh of wide lines.
6. Finally perform the same for the side view of the room. This will again look like a mesh of wide lines.
7. At each of these lines a standing wave can be excited very good. Each of these lines corresponds to a resonance frequency that can be calculated and should be attached to each line.
8. The 'art' of choosing loudspeaker and listening positions is:
• To avoid IN ANY CASE the combination 'good to excite' and 'good to hear' for ALL frequencies
• To avoid the combination 'can not excite' and 'can not hear' for ALL frequencies
• the best compromise are the combinations 'excite normal' and 'hear normal'.

Please find programs for optimum speaker placement and listener position on the Links page.

In reality people don't enjoy music in rectangular rooms without furniture where all areas (walls, floor, ceiling) have a constant absorption over the surfaces. Therefore the results of room simulation programs can only approach the real world situation.
Furthermore it must be distinguished between the reproduction of quasi stationary low frequencies (like organ or bowed bass) and impulsive signals with low frequency content (e.g. bass drum, or slapped bass). In the first case room resonances can be very annoying, in the second case the room as a resonant system does not start to ring.

I use my program SB_OCT to measure the resonance frequencies of the actual loudspeaker/listener configuration with pink noise excitation (this represents more the impulsive excitation) or my program SINUSGEN to excite individual resonance frequencies and to get an impression of the local distribution of the sound pressure (worst case of stationary excitation).