The Physics of Music:Environmental Acoustics

James Bernhard

In the first part of the semester, we discussed the fact that soundwaves go through three stages:

I Production

I Transmission

I Reception

At the start of the semester, we worked digitally, which allowed usto focus on reception

We then shifted our focus to sound production

We now turn our attention to transmission. . .

When a sound is emitted unobstructed, it emanates in all directions

In open air, sound intensity level drops off by about 6 dB when thedistance from the source is doubled

Human beings have an excellent ability to localize sounds, ordetermine their source

For sounds of low frequency, we observe a slight difference in thetime of arrival (or the phase, for steady sounds) at our two ears

For sounds of higher frequency (above about 1000 Hz), weperceive a difference in the sound level in our two ears because ofthe sonic shadow of our head

This sonic shadow isn’t as pronounced for low frequency soundsbecause (having a longer wavelength) they diffract around thehead more strongly

Human beings generally find it easier to localize high-pitchedsounds than low-pitched sounds

If the sound is indoors, it will reflect off the walls, ceiling, and floorto some degree

Some terms we use to classify sound waves that reach a listenerare:

I direct sound consists of sound waves that propagate fromsource to listener without being reflected

I reverberant sound or reverberations consists of sound wavesthat reach the listener after being reflected

I early sound refers to the first group of reflected sound waves,which reach the listener within about 50-80 ms of the directsound

Early sound waves tend to arrive individually, while reverberantsound waves are all clustered together, as pictured at theAV Info website

Direct sound is much easier to localize and analyze, but the arrivalof reflected sound complicates perception

Early reflections will have essentially the same spectrum and timeenvelope as the direct sound, and if they arrive within about 50-80ms of the direct sound, we do not perceive them as separate sounds

Instead they reinforce the direct sound

The perceptual limit is about 50 ms for rapidly changing soundssuch as speech, but is close to 80 ms for slowly varying music

When we localize a sound that is reinforced by reflected sound, webase our localization on the first sound to arrive (which isordinarily the direct sound) if

I successive sounds arrive within about 35 ms

I the successive sounds have spectra and time envelopesreasonably similar to the first sound

I the successive sounds are not too much louder than the firstsound

This is called the precedence effect (or the Haas effect)

In a study of the world’s leading concert and opera halls, Beranek(1996) found that concert halls are described as “intimate” whenthe delay time between the direct and first reflected sound is lessthan 20 ms

In a traditional rectangular-shaped auditorium, the first reflectionfor most listeners comes from the nearest side wall, although thosenear the center may get it from the ceiling

In larger halls, some listeners may be far enough from the walls andthe ceiling that they don’t receive the first reflected sound in thistime interval

To help alleviate this, reflecting surfaces of some type are oftensuspended from the ceiling

However, recent studies have shown that early reflections fromceilings, ceiling reflectors, and side walls are not perceptuallyequivalent in judging “intimacy” of a hall

One study showed a high preference among listeners for concerthalls with ceilings sufficiently high that the first reflected soundcomes from a side wall

Other studies have found that if the total energy from side wallreflections is greater than the energy from overhead reflections,then the hall has a desirable “spatial responsiveness” or “spatialimpression”

The behavior of reverberant sound is far too complicated to bedescribed by a single number

However, if you had to choose a single number to describe it, thereverberation time at midfrequency (500 to 2000 Hz or so) gives afair indication of the “liveliness” of a hall

The reverberation time of a sound is the time for it to decrease by60 dB; look at the decibel level chart in wikipedia to see what thiscorresponds to

Reverberant sound, like the early sound, reinforces the direct soundand adds to the overall loudness (which can be important in alarge auditorium), but too great a level of reverberant sound canresult in a loss of clarity

Direct sound should be substantially louder than reverberant soundat all locations in a hall, which sometimes calls for electronicreinforcement of direct sound

For a full-size symphony orchestra, most listeners find the directsound level to be optimal when they are seated about 20 m (60 ft)from the source, which would be at the center of many of theworld’s leading concert halls

In a bare room where all surfaces absorb the same fraction of thesound that reaches them, the reverberation time is proportional tothe room volume divided by the room’s surface area

In this idealized model, larger rooms have longer reverberationtimes (as is generally true)

However, if some surfaces absorb a higher fraction of sound, thenthat will decrease the reverberation time; also, air itself absorbssound too

With these complications, a more accurate formula forreverberation time in a large concert hall is:

reverberation time = 0.161V

A + kV,

where V is volume, A is the “total absorbtion” coefficient of thehall, and k depends on the temperature and humidity

Some criteria for good acoustics:

I Adequate loudness

I Uniformity

I Clarity

I Reverberance, or liveliness

I Freedom from echoes

I Low level of background noise

Note that reverberance varies with frequency; it is often desirableto try to obtain reverberance specifcally for low frequencies, as thehyperphysics website describes

The scientific principles behind acoustic design of concert halls arewell studied and fairly well understood

In spite of this, some concert halls (both old and new) haveacoustical problems

The most common problem leading to these is poorcommunication among architects, acoustical designers, buildingcontractors, and musicians who use the hall

Music and acoustics developed largely separately, so they oftenhave different vocabularies

In his 1996 book on concert halls, Beranek attempts to bridge thelanguage gap by defining some terms in a way that both musiciansand acousticians can understand them, such as:

I intimacy or presence: music played in the hall gives theimpression of being played in a small hall.

I reverberation: sound that persists in the room after the tonehas stopped. Liveliness refers to reverberation for tones aboveabout 350 Hz.

I spaciousness in the sense of auditory source width (ASW): thesound appears to emanate from a source wider than the visualwidth of the source.

I spaciousness in the sense of listener envelopment (LEV): thereverberant sound appears to come from all directions

I clarity: the degree to which discrete sounds in a musicalperformance stand apart from each other.

I warmth: the liveliness of the bass, or the fullness of the basstones (about 75-350 Hz) relative to the midfrequency tones(350-1400 Hz). Dark also refers to a strong bass.

Each concert hall is better suited to some types of music morethan others

For example, the Royal Festival Hall in London is considered “dry”(with a 1.5 s reverberation time), which can be a goodenvironment for chamber music and Baroque music

This has recently be modified electronically with some “assistedresonance”

The Royal Albert Hall in London has a long reverberation time(about 2.6 s, or up to 3.4 s for low frequency sounds) and so worksbetter for music such as Tchaikovsky’s 1812 Overture

In addition to the general criteria for good acoustics, concert hallshave other desirable aspects, such as:

I spaciousness, in both the senses of auditory source width andlistener envelopment

I slow initial rate of decay, which turns out to be moreimportant than the total reverberation time in assessing thedesirability of the hall

Some things to avoid in concert hall design:

I echoes (sounds not appearing until after about 50 ms), whichare usually due to the rear wall

I flutter echoes (a series of echoes in rapid succession), whichare often due to reflections between two highly reflectiveparallel surfaces

I sound focusing, which can be caused by reflection from a largeconcave surface

I sound shadows, which can occur under balconies at the rear ofa hall

I background noise

For more on sound focusing, let’s look at the hyperphysics website

A study of 22 European concert halls by Schroeder, Gottlob, andSiebrasse (1974) found:

I The greater the early decay time, the more desirable the hall,up to a reverberation time (determined from the early decaytime) of 2 s; above 2 s, the opposite

I narrow halls were generally preferred to wide ones

I listeners showed considerable preference for a high binauraldissimilarity, as might result from a high degree of asymmetricsound diffusion

I halls with less definition were preferred, where definition refersto the ratio of energy in the first 50 ms to the total energy ofthe sound

Many halls considered to have good acoustics have a “shoebox”design, which has given rise to many more halls of this shape

Avery Fisher Hall in New York City (originally called PhilharmonicHall and housed in the Lincoln Center for Performing Arts) makesan interesting case study in acoustical design

It opened in 1962 and underwent many renovations between 1962and 1976, when it was completely rebuilt

It was designed by architect Max Abromovitz after an extensiveresearch study by acoustician Leo Beranek of the world’s leadingconcert halls

Acoustical expertise was provided by Beranek’s firm

The 1962 opening was to be spectacular, but most musicians andlisteners were disappointed by some major defects:

I weak bass

I lack of liveliness

I echoes from the rear wall

I inadequate sound diffusion

I poor hearing conditions for the music on stage

Scientists from Bell Telephone Laboratories were called on toevaluate the acoustics, and a distinguished committee of acousticalconsultants were called on to recommend improvements

Changes made during the summers of 1963, 1964, 1965, 1969, and1962 cost more than $2 million and improved the hall some

In 1975, the hall was completely redesigned more along the lines ofBoston’s Symphony Hall and the more recent Kennedy Center inWashington and Orchestra Hall in Minneapolis, costing more than$5 million

So what went wrong?

Beranek maintains that the final plans were expanded and modifiedwithout his consent or that of the orchestra

Seating capicity was enlarged from 2400 to 2600, and the sidewalls were spread out to give a more “modern” fan shape

The adjustable ceiling was eliminated for financial reasons, as weresome irregularities on the side walls that were to serve as sounddiffusers

136 panels (“clouds”) were suspended from the ceiling to provideearly reflections, but later research indicated that ceiling reflectionsare not as desirable as wall reflections for listeners’ assessment ofthe hall

Also, the designers had planned to try to optimize some acousticalparameters during a “tuning week” after the hall was built

Overall, the hall had insufficient diffusion of sound, which resultedin a decay curve having a different rate at the start and toward theend

The total reverberation time was fine, but the initial decay was toorapid, which gave the impression of dryness

Buildings besides concert halls have some other considerations

Churches and synagogues are supposed to accomodate bothspeech and music, which leads to a difficulty in trying to settle ona good reverberation time

Historically, most of the cathedrals and churches in Europe havelong reverberation times, giving emphasis to music over speech

Nowadays, background noise, such as from HVAC systems, is animportant consideration

Classrooms also have such considerations: reverberation, HVACbackground noise, and noise from outside the classroom