Sound Part II  Music

What is the study of sound called?  Acoustics

What is the difference between music and noise?  Music: Sound that follows a regular pattern; a mixture of frequencies which have a clear mathematical relationship between them.clear mathematical relationship  Noise: Sound that does not have a regular pattern; a mixture of frequencies whose mathematical relationship to one another is not readily discernible.

SOURCES OF SOUND Sound comes from a vibrating object. If an object vibrates with frequency and intensity within the audible range, it produces sound we can hear. MUSICAL INSTRUMENTS Wind Instruments: Open Pipe: flute and some organ pipes Closed Pipe: clarinet, oboe and saxophone String Instruments : guitar, violin and piano Percussion Instruments: Drums, bells, cymbals

As a string vibrates, it sets surrounding air molecules into vibrational motion. (called forced vibrations) The frequency at which these air molecules vibrate is equal to the frequency of vibration of the guitar string. Forced vibrations: the vibration of an object caused by another vibrating object. AKA Resonance

Standing Waves  A type of ____________ resulting in ____________. Created when periodic waves with equal amplitude and wavelength reflect and superimpose on one another. fendt.de/ph14e/stwaverefl.htm reflection interference

Cont’d

 Nodes: appear __________ and are due to ______________ interference.  Antinodes: appear to ___________ and are due to _______________ interference. stationary destructive constructive vibrate

Standing Wave: A result of interference. Occurs at harmonic frequencies  only created within the medium at _______ _________ of vibration (harmonic frequencies)  as frequency of the wave _____________, number of nodes and antinodes ___________ in the same amount of space specific frequencies increases

Ruben’s Tube  Ruben's Tube - YouTube Ruben's Tube - YouTube

Standing Waves The nodes and antinodes remain in a fixed position for a given frequency. There can be more than one frequency for standing waves in a single string. Frequencies at which standing waves can be produced are called the natural (or resonant) frequencies.

Demo mini-wiggler A guitar or piano string is fixed at both ends and when the string is plucked, standing waves can be produced in the string. Standing waves are produced by interference Resulting in nodes an antinodes 2-antinode

When an instrument produces sound, it forms standing waves and resonates at several related frequencies.  Fundamental Frequency(1 st harmonic): the ___________ frequency that an instrument vibrates at. Defines it’s ________  Overtones: Other frequencies the instrument resonates at  Harmonics= Overtones that are whole number multiple of the fundamental frequency.  The harmonics enhance the quality lowest pitch

Sound Spectrum  Intstruments do not produce a single sound wave

Superposition of many sine waves sawtooth wave f = 500 Hz (A = 1)f + 2f (A 2 = 1/2) f + 2f + 3f (A 3 = 1/3)f + 2f + 3f + 4f + 5f (A 5 = 1/5) 10 harmonics

A sound is the sum of its parts. Piano Fundamental only Harmonics 1 & 2 Harmonics 1, 2, 3 Harmonics Harmonics Harmonics Full sound

 Physical Science: Sound | Discovery Education THe Piano Physical Science: Sound | Discovery Education THe Piano

Boundary Conditions on a String Since the ends are fixed, they will be the nodes. The wavelengths of the standing waves have a simple relation to the length of the string. lowest fundamental frequency The lowest frequency called the fundamental frequency (1 st harmonic)has only one antinode. That corresponds to half a wavelength:

The other natural frequencies are called overtones. They are also called harmonics and they are integer multiples of the fundamental. first harmonic The fundamental is called the first harmonic. second harmonic The next frequency has two antinodes and is called the second harmonic.

The equation for strings is f – frequency in hertz n – number of harmonic L – length of string in meters V – velocity in medium in meters/sec λ - wavelength in meters - n can be any integer value greater than one.

A wave travels through a string at 220m/s. Find the fundamental frequency (1 st Harmonic) of the string if its length is 0.50m.  v= 220 m/s  L = 0.5 m  n = 1  f = nv/2L  f =(1)(220 m/s) /(2)(0.5m)  f = 220 Hz

Find the next two frequencies (2 nd and 3 rd harmonics) of the string.  Second Harmonic  Third Harmonic

A wave travels through a string at 220m/s. Find the fundamental frequency (2nd Harmonic) of the string if its length is 0.50m.  v= 220 m/s  L = 0.5 m  n = 1  f = nv/2L  f =(2)(220 m/s) /(2)(0.5m)  f = 440 Hz

A wave travels through a string at 220m/s. Find the fundamental frequency (3rd Harmonic) of the string if its length is 0.50m.  v= 220 m/s  L = 0.5 m  n = 1  f = nv/2L  f =(3)(220 m/s) /(2)(0.5m)  f = 660 Hz

What is the pattern that you are seeing? What do you think the frequency is for the 4 th harmonic?

 If you had a string that was 10 m long and it was vibrating in the 5 th harmonic, how would you solve for wavelength?  v/λ = nv/2L  Rearrange to solve for λ  2Lv/nv = λ  λ = 2L/n  λ = 20m /5 = 4m

When string is longer, the  Wavelength is  Longer  Therefore the frequency is  Lower

The sounds produced by vibrating strings are not very loud. Many stringed instruments make use of a sounding board or box, sometimes called a resonator, to amplify the sounds produced. The strings on a piano are attached to a sounding board while for guitar strings a sound box is used. When the string is plucked and begins to vibrate, the sounding board or box begins to vibrate as well (forced vibrations). Since the board or box has a greater area in contact with the air, it tends to amplify the sounds. On a guitar or a violin, the length of the strings are the same, but their mass per length is different. That changes the velocity and so the frequency changes.

Frequency in string depends on  Length of string: inverse or direct?  Inverse  As string length goes up frequency decreases  Tension: inverse or direct?  Direct  As tension increases frequency increases (shortening string)  Thickness: inverse or direct?  Inverse  As thickness increases frequency decreases

 The speed v of waves on a string depends on the string tension T and linear mass density (mass/length) µ, measured in kg/m. Waves travel faster on a tighter string and the frequency is therefore higher for a given wavelength. On the other hand, waves travel slower on a more massive string and the frequency is therefore lower for a given wavelength. The relationship between speed, tension and mass density is a bit difficult to derive, but is a simple formula:  v = T/µ  Since the fundamental wavelength of a standing wave on a guitar string is twice the distance between the bridge and the fret, all six strings use the same range of wavelengths. To have different pitches (frequencies) of the strings, then, one must have different wave speeds. There are two ways to do this: by having different tension T or by having different mass density µ (or a combination of the two). If one varied pitch only by varying tension, the high strings would be very tight and the low strings would be very loose and it would be very difficult to play. It is much easier to play a guitar if the strings all have roughly the same tension; for this reason, the lower strings have higher mass density, by making them thicker and, for the 3 low strings, wrapping them with wire. From what you have learned so far, and the fact that the strings are a perfect fourth apart in pitch (except between the G and B strings in standard tuning), you can calculate how much µ increases between strings for T to be constant.

WIND INSTRUMENTS Wind instruments produce sound from the vibrations of standing waves occur in _________of _______ inside a pipe or a Open Pipe Boundary: Closed Pipe Boundary: Open at both ends pipe Closed at one end pipe Antinode to antinode Node to antinode columns air

So for an Open tube, since each harmonic increases by ½ a wavelength, calculation is same as for string. However use velocity of sound in air (usually 340 m/s) 1 st Harmonic is ½ of a wavelength

For a half-closed tube Different than open pipes due to boundary. Start at ¼ λ and build by ½ a λ. Use velocity of sound in air (usually 340 m/s) 4 Why a 4? 1 st Harmonic is ¼ of a wavelength

a) For open pipe The harmonics will be all multiples of the fundamental n = 1, 2, 3, 4, 5 … b) For closed pipe The harmonics will be the odd multiples of the fundamental n = 1, 3, 5, 7, … HARMONICS

both ends Ex 6: A pipe that is open at both ends is 1.32 m long, what is the frequency of the waves in the pipe? v = 340 m/s L = 1.32 m = (1) (340) 2 (1.32m) = Hz Ex 7: What if it was closed at one end? = (1) (340) 4 (1.32m) = Hz f = nv 4L f = nv 2L

Ex 8: An organ pipe that is open at both ends has a fundamental frequency of Hz when the speed of sound in air is 331 m/s. What is the length of this pipe? f' = 370 Hz v = 331 m/s = 0.45 m f = nv 2L 370 = (1)(331) 2 L L = (1)(331) 2(370)

How can you change the fundamental frequency of a wind instrument?  Change the length of the air column: open and close valves  As the length shortens, the wavelength gets  Shorter  Which means the frequency gets  Higher  And the pitch is  higher

Beats…..or how to tune a guitar!  Beat _____________ refers to the rate at which the volume is heard to be ____________from high to low volume.  It is due to the interference effect resulting from the ____________________ of two waves of slightly different frequencies propagating in the same direction frequency oscillating superposition

 The beat frequency between two sound waves is the absolute difference in the frequencies of the two sounds.  f beat = | f A - f B |  Ex I: Given a sound at 382 Hz and a sound at 388 Hz:  f beat = 6Hz  The human ear cannot detect  beat frequencies of greater than 10Hz.  Musical instruments are tuned to a single note when the beat frequencies disappear.

 The Beat... The Beat...  Beats Beats  Auditory Illusion Auditory Illusion

Palm Pipes Activity  An example of a closed pipe