Increasing the intensity of a sound by a factor of f:

A] multiplies the SIL by f, regardless of the intensity

B] adds a constant to the SIL, regardless of the intensity

C] neither; it depends on the initial intensity

Adding a constant (say 0.2 W/m2) to the intensity of a sound:

A] multiplies the SIL by the same factor, regardless of the intensity

B] adds the same constant to the SIL, regardless of the intensity

C] neither; it depends on the initial intensity

Sound A has a SIL (in bels) that is twice sound B.

The intensity of sound A is:

A] twice that of sound B

B] four times that of sound B

C] Cannot determine the ratio of intensities

It will help to remember this…

With SILs, we talk about differencesWith Intensities, we talk about ratios

A SIL difference corresponds to an intensity ratio

Demonstration on the dBA scale.

Very Low frequency is quieter at the same I.

The ear as a machine.

Archimedes: Give me a place to stand and I can move the earth!

Simple lever

Take a guess: if I want the force output to be twice the force input, x2 should be:A] half x1 B] the same as x1 C] twice x1

Answer: half x1. The product of the force times the “moment arm” is the same.

Simple lever

Note: If the ends move, the end with the smaller force moves farther, so work IN = work OUT ! Energy is conserved.

A hydraulic lever.

Note that the force F1 must be applied over a great distance to raise the car a little bit.

Work IN = Work OUT

Energy is conserved

The human ear. Where are the levers?

Malleus moves 1.3x as far as the stapes. Assuming no energy losses, what is the force on the oval window,compared with the force on the eardrum (& malleus) ?

A] force on oval window is 1.3 times larger than force on eardrumB] force on oval window is 1.3 times smaller than force on eardrumC] force on oval window is equal to force on eardrum

This is the the opposite of the hydraulic lift. There, we built a system where the pressure was the same and coupled input and output, and the force was “leveraged”.

Here, the force is the same and couples input and output, and the pressure is “leveraged”.

Ignore for a moment the 1.3x increase in force provided by the ossicular lever, assume force IN=force OUT. The area of the eardrum is about 20x the area of the oval window. By what factor is the pressure amplitude in the perilymph greater than the pressure amplitude in the air?A] 400XB] 20XC] 1X (pressure amplitude is the same)

The total “gain” of this PRESSURE amplifier is 1.3 x 20 = 26x.

Let’s consider the real ear, vs. a hypothetical ear in which there is no pressure gain. What improvement in sensitivity to sound INTENSITY, in dB, is there with the real ear? (Use a calculator)

A] none, because energy is conserved

B] about 14 dB

C] about 26 dB

D] about 28 dB

Hair cells. (Nothing to do with Hair Club for Men, Clairol, etc.)

How does sound information get “encoded” in neural signals?

Given that nerves are “digital” (either firing or quiescent), how would an engineer design an ear?

You could have nerves that fire if the pressure rises above (or falls below) their threshold. This is called the “telephone theory”

This is NOT how God (or evolution) built your ears.

Waveform perception is not yet fully understood!!

There are good reasons why God didn’t build your ears to sense absolute pressure levels.

1. It’s very hard to do. You can measure force by, for example, seeing how far a spring stretches. But for pressure to generate a net force, it must be unbalanced.

2. Lots of things that don’t carry especially useful or urgent information, like barometric pressure, would be sensed, and might interfere with hearing the roaring of the lion next to you!

Homework is due todayFor the exam, please sit in seat #s that are divisible by 3

Homework due NEXT Thursday is chapter 6Qs2, 6, 11, 12, 13, 16 And 1 additional Question posted on the web.

Hair cells (and the basilar membrane) are (damped) harmonic oscillators.

When they are driven at their resonant frequency, the respond strongly (and send a lot of nerve impulses.)

So the ear doesn’t sense sound directly, it senses the frequencies present in sound. (mostly…)

Close to the oval window, the basilar membrane vibrates most for high frequencies.

Close to the helicotrema, it vibrates most for low frequencies.

The idea that different places in the cochlea sense different frequencies is called

Place TheoryHelmholtz 1863

Clearly, there’s more to hearing than this.For one thing, the response curves are much broader than our actual ability to sense pitch!

(We can sense 1 Hz difference in a 1 kHz pitch!)

We also know that hair cells send a signal EACH TIME the bundle of cilia is tipped… in other words, at each peak of fluid displacement, provided it is large enough.

So hair cells send a signal periodically (in the physics sense); i.e. once per period of the sound wave.

The idea that the period of the sound wave is measured is called… wait for it…

Periodicity Theory

Note that place theory is not wrong, it just isn’t complete.

Place & Periodicity theories together do very well, but there is clearly more still… modern theories of perception include “pattern recognition.”

Perception and “Just Noticiable Differences”

How close can two tones be in frequency (pitch) or volume (SIL) and be distinguished?

Let’s see how many people can tell which tone is higher in pitch.

A] tone A is higher in pitchB] tone B is higher in pitch

How many of you have ESP?A] headsB] tails

Perception and “Just Noticiable Differences”

How close can two tones be in frequency (pitch) or volume (SIL) and be distinguished?

Volume: Ask 100 people which is louder, A or B. (They are not allowed to say the tones are equal.) Suppose A has an SIL = 60.00 dB and B has an SIL of 60.01 dB. In your test, 50 people say A is louder and 50 people say B is louder.

How many people could really tell that B was louder?A] noneB] 25C] 50

The % correct on any forced two-choice experiment can never be lower (when the sample size is large) than 50%.

Suppose 80% get it right. How many actually detected the difference? Let’s work it out.

Of those who can’t detect a difference, the same number will get it wrong as right.

So in this case, what % can’t detect a difference, but got it right (by luck!)A] 0 % B] 10% C] 20% D] 40%

So in this case, what % can’t detect a difference, but got it right (by luck!)A] 0 % B] 10% C] 20% D] 40%

Answer C. Since 20% got it wrong, the same number got it right just by chance.

So how many people can truly distinguish the two tones?A] 40% B] 60% C] 80%

Remember: Half of those who can’t distinguish WILL choose correctly.

Suppose 20% of the people can truly tell there is a difference between two tones. What % will get the correct answer on a forced two-choice experiment?

A] 20%

B] 40%

C] 50%

D] 60%

E] 70%

The usual criterion for a just noticeable difference JND is that 50% of the population can truly detect a difference.

This is 75% correct on a forced two-choice experiment.

The JND in SIL is between a half and one dB.

1 dB is an intensity ratio of 100.1 = 1.26, i.e. an increase of 26% in intensity.

JND for frequency is about 1 Hz (for frequencies < 1 kHz), but gets poorer > 4 kHz.

Note that a 1 Hz JND represents about a semitone at 20 Hz, but MUCH less than a semitone at 1 kHz.

W/m2

SIL

Hz

We might wish to “quantify” the psychological variables (like loudness.)

This is a little like asking someone to “assign a number to the level of pain you are feeling.”

On the assumption that human perception of sound is universal enough for this quantification to be worthwhile, we can try…

We can

1) Play two tones in succession, ask the subject “how much louder was tone 2 than tone 1? Ratio estimation

2) Ask the subject to adjust the volume knob until a tone is twice as loud as a test tone. Ratio production

1 sone is the loudness of 1 kHz sine wave at 40 dB.

2 sones is twice as loud. 3 sones is thrice as loud, etc.

If asked to participate in such an experiment, one (probably the most appropriate) response would be to tell the experimenter:

“You’re nuts. How can I say one sound is ‘twice as loud’… you think I got a meter in my head? How about asking me whether one color is twice as red as another?”

But, in fact, most folks don’t. Instead, they do their best, whatever that means.

The results show that, approximately, loudness halves for every decrease of about 6 dB. In other words, it seems that when the experimenter forces subjects to halve the loudness, they are thinking “what would it sound like if I were twice as far away?”

This shows (IMO) that people are smarter than scientists.

Thin line is6 dB = 2x loudness change

Fletcher-MunsonDiagram

Contours of equalloudness sine waves reported (alas) in phons.

1 kHz sineat 60 dB SIL is the same loudness as 4 kHz at 50 dB.

But how loud is it? (in sones?)

To get the loudness of any sine wave, do 2 steps.

Read the phons off the F-M diagram, and then use the 1 kHz line on the sone/dB chart to find the sones.

60 phons is loudness of 60 dB at 1 kHz.

Off this diagram(the “sone dB conversion chart”) read that 60 dB at 1 kHz is ~ 6 sones.

Timber - characteristic “sound” of an instrumentRelated to the waveform.

We also recognize different instruments by their transients, the beginnings and endings of notes.Initial transients, when the waveform is rapidly changing, vary from 0.02 s for an oboe to 0.09 s for a violin.

Bach doubled violin parts on the oboe to achieve greater precision in the attack.

Ingredients of Music

Tempo (pl. Tempi)Largo .. Larghetto .. Adagio .. Andante .. Allegro .. PrestoM.M. = metronome marking… musical beats per minute

MeterArrangement of time unitse.g. 3/4, 4/4, 6/8Bottom #: note typeTop #: how many in a measure

RhythmPattern of weak & strong “beets” (pun)Syncopation

Melody, Harmonic, & ScalesScales are the allowed pitches. In western music, we use 12 notesper octave. We space them equally: “equal tempered scale”.

Twelve-semitone scale is called the chromatic scaleA semitone interval is a freq ratio of 1.05946. Why?

Major & Minor scales have 7 notes (the octave is the 8th)

One note following another: melodic intervalTwo notes together: harmonic intervalThree notes together: chord

Names of intervals come from the 7 note scales:

Octave Fifth FourthThird etc.

http://webphysics.davidson.edu/faculty/dmb/JavaSounddemos/harmonics.htm

Intervals

All major intervals correspond to a major scale,But the minor 2nd does not correspond to a minor

scale.

A minor second interval is a frequency ratio of 1.05946.

What is the frequency ratio of a major second?

A] 1.11892

B] 1.05946 x 1.05946 = 1.12245

C] 2.11892

Harmonic series (of notes):

A fundamental frequency and all its integer multiples

Example:A110, 220, 330, 440, 550, 660, 770, 880… A110, A220, ~E329.6, A440, ~C#554.4, E660, ?? , A880…

Given this harmonic series starts at A110, what is the approximate frequency of this note?

A] 880 HzB] 990 HzC] 110 Hz

Is 990 Hz the exact frequency of this B?

A] YesB] No

Is 990 Hz the exact frequency of this B?

B] No. It’s a major second above A880, so it is exactly1.059462 x 880 = 987.7608… Hz