Table of Contents
- Sound radiated by a point source is reflected by the rigid wall
- Image sound sources due to reflection:
The reflections act as if they were radiated from another identical point source behind the wall (at the same distance from the wall as the real sound source).
- Sound field is built up from the direct sound and a vector sum of contributions of all the images.
- Different approaches for different frequency ranges in small room.
- Wavelength large compared to room dimensions:
- Wavelength comparable to room dimensions:
- wave acoustics, standing waves, modes
- resonance boost of loudness
- Wavelength too short for wave acoustics and too long to be considered as a ray:
- diffusion and diffraction of sound dominate
- Wavelength substantially smaller than room dimensions:
- sound rays: "The angel of incidence = the angel of the reflection"
- Room resonances, natural frequencies, standing waves
- Two parallel reflective walls (of infinite extent) and air between them can be considered as a resonant resonant system.
- Frequency of resonance fr = c/2L, where c is the speed of sound and L is spacing between the walls.
- Resonance also at multiples of fr, at frequencies 2fr, 3fr, ... (harmonic frequencies)
- Modes and their intercation affects room response.
- Wave acoustics in rectangular rooms
- From wave equation (stated by Rayleigh in 1869) after several steps solutions for sound in rectangular enclosures.
- Calculation of the permissible frequencies corresponding to the modes of the rectangular enclosures:
where p,q,r = 0,1,2,3, ...., c is the speed of sound, L the length of the room, W width, and H height. sqrt means square root.
- Axial modes involve reflections from two surfaces of the room.
- Tangential modes from four surfaces.
1/2 of the energy of axial modes.
- Oblique modes from six surfaces.
1/4 of the energy of axial modes.
- Axial modes have the greatest affect to the room response, and at low frequency.
But tangential and oblique modes have some effect on the room's sound pressure pattern.
- Number of normal modes increase with frequency
=> Smoother room response in high frequencies.
- Modes decay at different rates.
- Mode decay depends on how absorbing material is distributed in the room.
- Reverberation in each octave bands depends on average of the decay of the several modes.
- The higher the octave center frequency, the more modes included.
- Each resonant mode is effective over a narrow band of frequencies.
- This bandwidth is determined by the amount of absorption in the room and is about 5-Hz wide for typical audio rooms.
- The bandwidth of the modes increase when the reverberation time shortens.
- A strong signal component may force closely adjacent modes into vibrating at the excitation frequency.
- When the excitating force is removed:
=> Adjacent modes decay at their natural frequencies.
- During decay period, new frequencies are radiated into the room.
=> A brief change of pitch.
- Reflected waves of the sound
- same waveform
- lower level and delayed
- any time when the level of echo signal momentarily attains the original sound level, the echo becomes audible
- For short delays (0-50 ms), echoes are perceived as part of the direct sound.
- The reverberation acts to increase the loudness of the sound
- The reverberation also changes the color of the sound ("liveliness of the room").
- Echoes with in 0-50 ms are not perceived as discrete, unless their level is increased.
- Human auditory system suppresses early reflections, occurring less than 50 ms after the direct sound.
- 1: Direct sound reaches the audience first.
- 2: Early reflected sound reaches the audience after the direct sound
- Early reflections are needed to give the feeling that someone is present at a space.
- 3: Reverberation reaches the audience from every direction (as a result of complex reflections).
- Reverberation creates the sense that performance is taking place in a large space.
- Pitch change during reverberant decay
<= shift of energy between normal modes
<= perceptual dependency of pitch on sound intensity
Here are notes Nick Zacharov made on Reverberation time.
- Reverberation = the tailing off of sound in an enclosure because of multiple reflections from boundaries.
- Sound pressure builds up as reflected components arrive later
- Sound decays exponentially after the source ceases.
- It takes finite time because of the finite speed of sound, losses at reflections, damping effect of the air, and divergence.
- Reverberation can be "good" or "bad" depending on its degree or on the circumstances.
- Symphony orchestra was recorded in an anechoic room and it sounded terrible (thin, weak, without resonance).
=> Music requires reverberation.
- Speech is more intelligble in rooms having lower reverberation times (long reverberation time maskes last consonants in the speech).
- Time needed for the mean-square sound pressure in a room to decay from steady state value by 60 dB after the sound source is suddenly turned off.
- Reverberation time is different for different frequencies.
- For high frequencies shorter reverberation time, mainly due to better high frequency absorption in the surface.
- There are equations to approximate reverberation time in a room. (Sabine, Eyring, Fizroy, ...)
- Reverberation time (T, in seconds) is directly proportional to the volume of the room (V, [m^3]) and inversely proportional to the room surface area (A, [m^2]) and the average coefficient of sound absorption (s):
- Developed at the turn of the century empirically
- Delayd signal (echo) is summed to the direct signal
=> the same effect as the signal were filtered with filter whose transfer function is
where d is delay.
- Amplitude response of this kind of filter is looking like "comb" having deep notches equally spaced.
- Sound reflected from surfaces important to perceived spaciousness
- reflected sound signals incoherent with direct sound
- proper level of reflections
- reflections arrive less than 50-100 ms after direct sound (or they will sound like echoes)
- reflections arrive from lateral directions
- If music or speech is percived in some place, room acoustics should be considered.
- feeling of the space
- sound direction
- In outdoor acoustics (i.e. free field), sound can travel unaltered in all directions
- geometrical spreading
- Indoor acoustics determines how sound acts in eclosed spaces
- reflective surfaces
=> sound energy better contained i.e. loudness is increased
- different approaches for different frequency ranges:
room modes / sound rays
- room modes: axial, tangential, oblique
colorations of sound
modal frequencies make up the room acoustics
- reflected wave of sufficient amplitude
- in small rooms, echoes exist physically, but not subjectively
- increase loudness
- Haas effect: our hearing mechanism integrates the sound intensities over short time intervals
- One part of a sound field
- good in moderate quantities, bad in excess