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Chapter 12 Parts of waves (review) Octaves Stringed Harmonics How to produce sound Open/Open Harmonics Open/Closed Harmonics Harmonics/Fundamentals

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Transverse waves Single wave pulse travels Transverse waves: The particles of the disturbed medium move perpendicular to the wave motion particle wave

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Longitudinal waves: The particles of the disturbed medium move parallel to the wave motion Longitudinal waves compression travels

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Basic Variables of Wave Motion Terminology to describe waves - Crest: “Highest point” of a wave - Wavelength : Distance from one crest to the next crest. - Wavelength : Distance between two identical points on a wave. - Period T: Time between the arrival of two adjacent waves. - Frequency f: 1/T, number of crest that pass a given point per unit time

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Sound - is a wave (sound wave) - Rarefied and compressed regions - Longitudinal wave - air molecules move back and forth

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Sound Waves Sound waves are longitudinal waves. They consist of compressed and rarified regions of gas (medium) We can hear (audible) frequencies from about 20 Hz (low) to 20,000 Hz (high). Infrasonic “sound” waves: below ~ 20 Hz Ultrasonic sound waves: above ~ 20,000 Hz The speed of sound in air: c ~ 343 m/s ~ 740 mi/hr ~ 0.2 mi/sec. (dry air, 68F)

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Question #1 A.1 mile B.2 miles C.3 miles D.4 miles E.5 miles It is a dark and stormy night. Lightning strikes in distance. You see the lighting, then, after ten seconds you hear the thunder. How far away did the lighting strike?

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Notes and their fundamental frequency Octaves: frequency doubles for each tone **Note** An octave will double in frequency each time and this is different than Harmonics

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For example: Find middle C (C4) on the chart to the right. Middle C has a frequency of Hz, one octave higher is C5 which has a frequency of Hz, two octaves higher (C6) has a frequency of Hz. Middle C can also be the fundamental frequency ( Hz) and this is the 1 st Harmonic, the 2nd Harmonic (f = Hz) is the same as one octave higher, but the 3 rd Harmonic (f = Hz) is NOT the same as two octaves higher.

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Creating standing waves: When two waves are traveling back and forth, under the right conditions (right frequency), we can create standing waves. Standing waves have stationary nodes and antinodes Examples we’ll talk about this chapter: - Standing waves on a string. - Standing waves in a pipe (open and closed).

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L 3f 1 2f 1 4f 1 5f 1 6f 1 frequency String Harmonics L … Length of string; n … harmonic v … velocity of sound

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L … Length of string n … harmonic Standing waves have stationary nodes and anti-nodes

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Fundamental Frequency String vibrates as a single arc, up and down –velocity antinode occurs at center of string This is the fundamental frequency mode Pitch (frequency of vibration) is –inversely proportional to string length

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Harmonics (Overtones) In addition, string can vibrate as –two half-strings –three third-strings –etc. These are higher-order frequency modes These modes have higher pitches – overtones

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Harmonics in a String In a string, the harmonic pitches are –two times the fundamental frequency (octave) –three times the fundamental frequency –etc. These integer multiples are called overtones A string harmonics will have all harmonics. i.e. 2 nd, 3 rd, 4 th, 5 th, etc.

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Producing Sound Thin objects don’t project sound well –Air flows around objects –Compression and rarefaction is minimal Surfaces project sound much better –Air can’t flow around surfaces easily –Compression and rarefaction is substantial Many instruments use surfaces for sound

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Open pipe:

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Fund. Frequency v… speed of sound v = 343 m/s in air at 20 °C

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Open/open tube

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A wave reflecting off of the boundary At an open boundary: the air bounces moving in and out of the boundary. motions

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Harmonic Vibrations for open-open In addition, column of air can vibrate as –two half-columns –three third-columns These higher-order modes are the harmonics Pitches are integer multiples of the fundamental Open/open tube has all integer multiples f,2f,3f,4f,5f OR 1 st, 2 nd, 3 rd, 4 th, 5 th, etc. (just like a stringed instrument) A open-open tube will have an anti-node at each open end

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open-closed pipe: Fundamental frequency:

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Open/closed tube

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Wave reflecting off of the closed boundary At a closed boundary: the wave reflects if it has a high pressure at the wall. The air compresses at the wall and then bounces back.

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Harmonic Vibrations for closed-open These higher-order modes are the harmonics Pitches are odd multiples of the fundamental Closed/open tube only has odd harmonics (e.g., clarinet) f, 3f, 5f, 7f OR 1 st, 3 rd, 5 th, 7 th, etc. A closed-open tube will have a node at the closed end

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You play an open organ pipe with a length of 1m. What is the fundamental frequency? A.1 Hz B.86 Hz C.172 Hz D.343 Hz E.686 Hz Now you close the pipe at one end. What will the frequency be then? A.1 Hz B.86 Hz C.172 Hz D.343 Hz E.686 Hz Question #2

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Standing waves or modes in a column of air The motions shown are air speeds One of these is a pipe that is closed on one end and the other is open on both ends. Which one is which? Question #3

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Which one has a lower fundamental frequency? Open/open or open/closed? Open/open open/closed Question #4

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Fundamental Frequency review Air column vibrates as a single object –Pressure antinode occurs at center of open column –Velocity antinode occurs at ends of open column Pitch (frequency of vibration) is –inversely proportional to column length –inversely proportional to air density A closed pipe vibrates as half an open column –pressure antinode occurs at sealed end –Velocity node occurs at the sealed end –frequency is half that of an open pipe

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