09 WS IV

1. 237 Hz, 474 Hz, 711 Hz2. 191 Hz, 573 Hz3. 311 Hz, 622 Hz4. 1.2m, .6m, .4m, .3m5. 414 Hz, 828 Hz, 1242 Hz6. 245 Hz, 735 Hz

Thur Tomorrow instrument showcase Quiz Monday

Yesterday we discussed terms associated with music and reviewed standing weaves in strings.

Answer Now: Calculate the wavelengths and

corresponding frequencies of the four longest waves standing in a 0.60 m string with a wave speed of 220m/s.

Sound Part II Pick up Sound II Note Sheet. Friday you had a quiz, Yesterday you completed the harmonics activity and turned it in. Complete and turn in warm ups

4/7 Warm Up #5 The rope below is 6 m long. How long

is it from point A to point B? What part of a wave is A-B?

A B

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.

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 pipesClosed 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.

http://www.walter-fendt.de/ph14e/stwaverefl.htm

reflectioninterference

Cont’d

Nodes: appear __________ and are due to ______________ interference.

Antinodes: appear to ___________ and are due to _______________ interference.

stationary

destructive

constructivevibrate

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

increases

Ruben’s Tube

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 beproduced are called thenatural (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 interferenceResulting in nodes an antinodes

2-antinode

When an instrument produces sound, it forms standing waves and resonates at several related frequencies.

Fundamental Frequency(1st 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 wavesSuperposition of many sine wavessawtooth wavesawtooth wave

f = 500 Hz (A = 1) f + 2f (A2 = 1/2)

f + 2f + 3f (A3 = 1/3) f + 2f + 3f + 4f + 5f (A5 = 1/5)

10 harmonics

A sound is the A sound is the sum of its parts.sum of its parts.

Piano

Fundamental only

Harmonics 1 & 2

Harmonics 1, 2, 3

Harmonics 1 - 4

Harmonics 1 - 5

Harmonics 1 - 6

Full sound

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.

The lowestlowest frequency called the fundamental frequencyfundamental frequency (1st 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.

The fundamental is called the first harmonicfirst harmonic.

The next frequency has two antinodes and is called the second harmonicsecond harmonic.

The equation for strings is

f – frequency in hertzn – number of harmonicL – length of string in metersV – velocity in medium in meters/secλ - 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 (1st Harmonic) of the string if its length is 0.50m.

v= 220 m/sL = 0.5 mn = 1 f = nv/2L f =(1)(220 m/s) /(2)(0.5m) f = 220 Hz

Find the next two frequencies (2nd and 3rd 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/sL = 0.5 mn = 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/sL = 0.5 mn = 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 4th harmonic?

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 antinodeNode 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)

1st Harmonic is ½ of a wavelength

For a half-closed tubeDifferent 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? 1st 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, …

HARMONICSHARMONICS

Ex 6: A pipe that is open at both endsboth ends is 1.32 m long, what is the frequency of the waves in the pipe?

v = 340 m/sL = 1.32 m

= (1) (340) 2 (1.32m)

= 128.79 Hz

Ex 7: What if it was closed at one end?

= (1) (340) 4 (1.32m)

= 64.39 Hzf = nv 4L

f = nv 2L

Ex 8: An organ pipe that is open at both ends has a fundamental frequency of 370.0 Hz when the speed of sound in air is 331 m/s. What is the length of this pipe?

f' = 370 Hzv = 331 m/s

= 0.45 m

f = nv 2L

370 = (1)(331) 2 LL = (1)(331) 2(370)

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... Beats Auditory Illusion

STOP HERE 2015

12.1 A saxophone plays a tune in the key of B-flat. The saxophone has a third harmonic frequency of 466.2 Hz when the speed of sound in air is 331 m/s. What is the length of the pipe that makes up the saxophone?

n = 3f3 = 466.2 Hzv = 331 m/s

12.5 A pipe that is closed on one end has a seventh harmonic frequency of 466.2 Hz. If the pipe is 1.53 m long, what is the speed of the waves in the pipe?

n = 7f7 = 466.2 HzL = 1.53 m

Widor Tocatta Tabernacle

http://www.youtube.com/watch?v=AXTNID_ysfA

Though the organ has been rebuilt and enlarged several times since 1867, the original, iconic casework and some of Ridges' pipes still remain in the organ today.[4] The current organ is largely the work of G. Donald Harrison of the former Aeolian-Skinner organ firm. It was completed in 1948 and contains 11,623 pipes, 147 voices (tone colors) and 206 ranks (rows of pipes).[4]

Open pipes vs Closed Pipes

Boundary conditions are different for pipes than for a string

Pipe organs, flutes, valve instruments are open pipes

Reed instruements, Chimes, bottles etc are closed pipes

If sound is resonating in a pipe, then what kind of wave is in the pipe?

Standing Wave

Open Pipe

An open ended instrument has both ends open to the air

Open vs Closed pipes (Flutes vs Clarinets)

Carrot Pan-flute - Waltz of wind – YouTube

Solo Trumpet Duet - YouTube

Open Pipes: Boundary conditions always antinodes

In an open pipe

What is the minimum part of a wavelength to have resonance(1st harmonic)?

How many wavelengths for the 2nd harmonic?

How many wavelengths for the 3rd harmonic?

Cont’d

Open Pipe Resonance

.5 λ λ 1.5 λ

Open Pipes

In open pipes, resonance occurs when the length is:

fundamental or 1st harmonic/ resonance: L = .5

1st overtone or 2nd harmonic/resonance: L =

2nd overtone or 3rd harmonic/resonance: L = 1.5

Same as strings….

What are the 3 lowest frequencies of an open organ pipe 40 cm long? Assume the speed of sound is 340 m/s.

Look at fundamental wave and determine relationship to length of pipe

Length = .5 λ λ = (length)/(.5) λ = (.4m)/(.5) = .8m F = v/λ F = 340m/s ÷ .8m = 425 Hz This is the fundamental frequency Now calculate the next two!!!!

2nd harmonic: 850 Hz

3rd harmonic: 1275 Hz

What it the relationship as the frequencies increase? What happens to their wavelengths?

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

Palm Pipes Activity

An example of a closed pipe

What is the difference between pitch and timbre?

If you are asked to calculate relative intensity, what are you calculating?

What are the boundary conditions for strings? For open pipes?

What is the wavelength for the fundamental frequency of an open pipe 6m long?

The fundamental frequency of a stringed instrument is 320 Hz. What is the frequency of the 2nd harmonic?

Closed Pipe A closed ended instrument has one

end closed off, and the other end open.

Beer Bottle Symphony Orchestra – YouTube

epic pvc - YouTube Funny skating bottle player – YouTube OK Go - Needing/Getting - Official

Video - YouTube

Closed Pipes: Boundary conditions always one node and one antinode

SOLVE NOW What are the two lowest frequencies of a closed pipe 35 cm long at 18oC? Quiz on Monday

Your Homework tonight is Unit 09 WS IV 6 problems. You must show work for the first

frequency. Not necessary for the others. Except for 2 and 6

SOLVE NOW What are the two lowest frequencies of a closed pipe 35 cm long at 18oC? Quiz on Monday

342 m/s at 18oC Now What? Look at fundamental wave and determine

relationship to length of pipe Length = .25 λ λ = (length)/(.25) λ = (.35m)/(.25) = 1.4m F = v/λ F = 342m/s ÷ 1.4m = 244 Hz This is the fundamental frequency Now calculate the next two harmonics!!!!

Closed Pipe Resonance

.25 λ .75 λ 1.25 λ

First or fundamental resonance

Second resonance

Third resonance

Closed Pipes

In closed pipes, resonance occurs when the length is:

fundamental or 1st harmonic/ resonance: L = .25 3rd harmonic/2nd resonance: L = .75 5th harmonic/3rd resonance: L = 1.25

only odd harmonics are present Resonances are found at half wave length intervals

2nd Resonance

L = .75 λ λ = (L)/(.75) λ = (.35m)/(.75) = 0.467m F = v/λ F = 342m/s ÷ 0.467m = 732 Hz What would be the 3rd resonance?

3rd Resonance

L = 1.25 λ λ = (L)/(1.25) λ = (.35m)/(1.25) = 0.28m F = v/λ F = 342m/s ÷ 0.28m = 1220Hz

What is the relationship between fundamental frequency and the next two resonances?

3x, 5x What do you think the next one

would be? 7x These are called the 3rd, 5th, 7th

harmonic and so forth.

STOP HERE

Complete question 6 on WS II WS III due Wednesday

Cont’d

Resonance website

An organ pipe closed at one end is 0.76 m long. The air temperature is 10 degrees Celsius. What fundamental wavelength does it reinforce?

What is its fundamental frequency?

Answer: 3.04 m

What is the speed of sound at this temperature? Answer: 337 m/s

Answer: 110.9 Hz

A pipe open at both ends is 0.76 m long and has a diameter of 5 cm. The air temperature is 10 degrees Celsius. What is the length of the vibrating air column?

Answer: 0.78 m

What fundamental wavelength will it reinforce? Answer: 1.56 m

What is the speed of sound at this air temperature? Answer: 337 m/sWhat fundamental frequency will it reinforce? Answer: 216 HZ

In addition to the air inside the pipe vibrating, the air just outside the pipe also vibrates.

Cont’d

The amount of air outside the pipe that vibrates is affected by the diameter. The length of the vibrating air column can be found using

L = ℓ + 0.4dL - length of the vibrating air columnℓ - length of the piped - diameter of the pipe

Interference Animation unitedstreaming.com - physical

science: sound coping with noise

An observer hears thunder 2 seconds after seeing the flash of lightning. If the speed of sound is 350 m/s, how far from the observer did the lightning strike?

Answer: 700 m

A field judge fires a starter pistol and hears the echo from the bleacher wall .8 s later. If the speed of sound is 343 m/s, how far from the wall is the judge?

Answer: 137.2 m

Musical Intervals: Whole number ratios

Octave: two notes with frequencies related by a ratio of 1:2 Ex. If an note has a frequency of 440 Hz, a

note one octave higher will have a frequency of 880Hz

Other intervals: major thirds. 2 pitches close together 4:5

ratio, C and E Chords. 3 pitches close together 4:5:6 ratio