THE PHYSICS OF MUSIC ♫

MUSIC• Musical Tone-

Pleasing sounds that have periodic wave patterns.

• Quality of sound- distinguishes identical notes from different instruments. http://

www.animations.physics.unsw.edu.au/jw/sound-pitch-loudness-timbre.htm

Beats- the change in sound intensity due to the interference of sound.

Beat Frequency- the number of maximum intensity points per second.

2 beats

Ex. A sound with a frequency of 400Hz interferes with a second sound. If this produces 20 beats in 5.0 seconds, what is the frequency of the second sound?

BF= 20beats/ 5 sec = 4 beats/sec

4 beats/sec = | 400Hz- f2 | = 396Hz or 404Hz

BF = # beats or BF = | f1 – f2 | second

STANDING WAVES

Two identical waves traveling in opposite directions.

N –node

A- antinode

MODES OF VIBRATION

Fundamental mode, lowest pitch. λ = 2L

First overtone, second harmonic, λ = L

Second overtone, 3 rd harmonic, λ = 2/3L

Third overtone, 4th harmonic, λ = 1/2L

HARMONICS

Whole number multiples of the fundamental frequency. Doubling the frequency will raise the pitch one octave (8 notes)

String Instruments

LAWS OF STRINGS

Law of Length: As the length of a string increases, frequency and pitch decreases.

Law of Diameter: As the diameter of a string increases, frequency decreases.

Law of Tension: As the tension on a string increases, frequency and pitch increases.

Law of Density: If a more dense string is used, the frequency and pitch decreases.

Woodwind and Brass

Use resonating air columns to make music.

RESONANCE IN AIR COLUMNS

Resonance occurs every half wavelength.

λ = 2L f1 = v/2L

L

λ = L f2 = v/L

L

λ = 2/3L f3 =3v/2L

L

Wavelength depends of the length and diameter of the resonating pipe.

λ = 2( L + 0.8d) L- length (m)

d- diameter (m)

Ex: An open plastic pipe will resonate at its lowest frequency when a tuning fork is held over it.

A) If the pipe has a length of 60cm and a diameter of 4.0cm what is the wavelength?

λ = 2( L + 0.8d)

λ = 2(0.6m + 0.8(0.04m)

λ = 1.264m

B) If the sound produced has a speed of 342m/s, what is its frequency?

(Lowest frequency is the 1st harmonic.)

f1 = v/2L

f1 = 342m/s / (2 x 0.6m)

f1 = 285 Hz

Just for fun!The Rubens Tube

• http://www.youtube.com/watch?v=gpCquUWqaYw

http://www.youtube.com/watch?v=M-021bsxM_k