This is PHYS 1240 - Sound and Music

Lecture 13

Professor Patricia Rankin

**** Not Available Wed 26 Office Hrs ***

Cell Phones silent

Clickers on

Physics 1240 Lecture 13

Today: CD recordings, Consonance and Dissonance,

Sound Intensity

Next time: Scales, Tutorial

physicscourses.colorado.edu/phys1240

Canvas Site: assignments, administration, grades

Homework – HW6 Due Wed February 26th 5pm

Homelabs – Hlab4 Not due till March 16th

Exam

Midterm – 1hr, Thursday March 5th – 3:30-4:30pm here

Accommodations – G135 March 5th – 3:30-5:00pm (need to be on list)

Mix of 10 short questions (5pt), 5 longer ones (10pt)

Short – more clicker like (quick)

Long – more math, closer to homeworks

Need calculator – cannot use phone, tablet, laptop

Based on first 12 lectures, first 6 homeworks and relevant book chapters.

Debrief - Fourier

• Periodic/harmonic series

• Sound envelope: graph of a sound’s amplitude over the duration of a note

• ADSR:

• Attack

• Decay

• Sustain

• Release

Debrief – Last lecture

Sampling Rate is how many samples taken per second

Nyquist Frequency = sampling rate / 2

Stereo – 2 channels

Largest possible amplitude = 2(bit depth)/2, smallest

amplitude is 1

Storage needed depends also on length of recording.

Nyquist Frequency – what you

can resolve (sampling/2)

Music

• Music: ordered patterns of sound in time

• Quadrivium (medieval curriculum) consisted of

arithmetic

geometry

music

astronomy

• Time signature: how many beats are in each measure

Examples:

Yankee Doodle 44

, Dave Brubeck’s “Take Five” 54

, Pink Floyd’s “Money” (_)

↔ numbers

↔ numbers in space

↔ numbers in time

↔ numbers in space and time

Scales

• Musical systems can have an arbitrary number of notes within one octave.

Must balance:

• Minimizing dissonance (more notes means more beats)

• Increasing complexity (fewer notes means less interesting)

• Pentatonic (e.g. minor blues scale, Javanese gamelan)

• Microtonal

• Consonance: when notes “sound good” together (sweet, pleasant,

acceptable)

• Dissonance: when notes “sound bad” together

(harsh, unpleasant, unacceptable)

Consonance and Dissonance

• Cause?

• Dissonance when 2 tones are within the same critical band (beats)

• Dissonance when upper harmonics interfere (beats)

• Consonance at “nice” whole number frequency ratios, when some

upper harmonics exactly match

Critical Bands

Two pure tones played together

Critical band: region of frequencies

inside of which you can’t distinguish

two tones

• Below 500 Hz critical bandwidth is about 100 Hz (±50 Hz)

• Above 500 Hz critical bandwidth is about 20% of the center frequency

(±10%)

Shostakovich’s

Fugue in A Major

(complete

consonance)

Messiaen’s

Catalogue

d'oiseaux

(complete

dissonance)

Clicker 13.1

If two tones of different frequencies are sounded together, which ratio of

frequencies would lead to the most dissonant sound?

A) 1/1

B) 2/1

C) 2/1

D) 1.5/1

E) 9/8

Clicker 13.1 C

If two tones of different frequencies are sounded together, which ratio of

frequencies would lead to the most dissonant sound?

A) 1/1

B) 2/1

C) 2/1

D) 1.5/1

E) 9/8

)(222 yxyx

xy22 y

x

Algebra with exponents

xyyx 22

x

x

2

12

Clicker 13.2

122 :A

2 :B

is equal to:

12

1

2 :D

21/ :C

theseof none :E

1212 2

Clicker 13.2 B

122 :A

2 :B

is equal to:

12

1

2 :D

21/ :C

theseof none :E

1212 2

Clicker 13.3

12 2 :A

212 )2( :B

is equal to:

12

1

2 :E

)2(1/ :C 12

212 )2(1/ :D

12

2

2

Clicker 13.3 B

12 2 :A

212 )2( :B

is equal to:

12

1

2 :E

)2(1/ :C 12

212 )2(1/ :D

12

2

2

Units – energy, power

Force = N (Newton, kgms-2)

Energy = force*distance (Nm = J (Joule))

Power = Energy/time (J/s = W (Watts))

Amplitudelitude

CompressionRarefaction

P A

The loudness of a sound isn’t directly related to the air’s

pressure; instead, what matters is the wave’s intensity

Intensity

Intensity is the amount of energy hitting a certain area in a certain time

Intensity is proportional to the square of the pressure amplitude

• If we double the amplitude, then we quadruple the intensity

I = 0.01 W/m2

I = 0.04 W/m2

Clicker Question 13.4

Two sound waves X & Y are measured to have intensities of 1 W/m2 and 9

W/m2, respectively. How do their pressure amplitudes compare?

A) X’s amplitude is the same as Y’s amplitude

B) X’s amplitude is 3 times larger than Y’s amplitude

C) X’s amplitude is 9 times larger than Y’s amplitude

D) Y’s amplitude is 3 times larger than X’s amplitude

E) Y’s amplitude is 9 times larger than X’s amplitude

Clicker Question 13.4 D

Two sound waves X & Y are measured to have intensities of 1 W/m2 and 9

W/m2, respectively. How do their pressure amplitudes compare?

A) X’s amplitude is the same as Y’s amplitude

B) X’s amplitude is 3 times larger than Y’s amplitude

C) X’s amplitude is 9 times larger than Y’s amplitude

D) Y’s amplitude is 3 times larger than X’s amplitude

E) Y’s amplitude is 9 times larger than X’s amplitude