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String and Air Instruments. Review – Standing waves in String Instruments Examples – String Instruments Longitudinal Waves in Air Standing Waves in Air Instruments (open-open) Standing Waves in Air Instruments ( open-closed) Summary Air Instruments (open-open, open-closed)

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## String and Air Instruments

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**String and Air Instruments**• Review – Standing waves in String Instruments • Examples – String Instruments • Longitudinal Waves in Air • Standing Waves in Air Instruments (open-open) • Standing Waves in Air Instruments (open-closed) • Summary Air Instruments (open-open, open-closed) • Examples – String and Air Instruments**Standing waves in String Instruments**• String anchored between 2 points and velocity fixed • Allowed opening widths • In general • Allowed wavelengths • ,2,3…. • Allowed frequencies Velocity is**Example 12-7**• Frequency of highest note • Frequency of lowest note • Ratio**Example 12-8**• Allowed wavelengths in string ,2,3…. • Frequency in Air Same as string v = 440 Hz. • Wavelength in Air Different because of different velocity**Longitudinal Waves in Air**• Traveling sound wave https://sites.google.com/site/physicsflash/home/sound • Pressure and Displacement Nodes/Antinodes**Standing waves in Air – open/open end (1)**• Display as transverse wave (easier to see) • Pressure wave node at both ends • Result: • Pressure wave node at both ends • Pipe length must be some multiple of ½ wavelength!**Standing waves in Air – open/open end (2)**• Animation – Pressure wave node at both ends http://faraday.physics.utoronto.ca/IYearLab/Intros/StandingWaves/Flash/sta2fix.html • Result: • Pressure wave node at both ends • Pipe length is some multiple of ½ wavelength!**Standing waves in Air – open/open end (3)**• Allowed widths • In general • Allowed wavelengths • ,2,3…. • Allowed frequencies Velocity is**Standing waves in Air – open/closed end (1)**• Display as transverse wave (easier to see) • Pressure wave node at one end, antinode at other • Result • Pressure wave node at one end, antinode at other • Pipe length is some odd multiple of ¼ wavelength**Standing waves in Air – open/closed end (2)**• Animation – Pressure wave node at end, antinode at other http://faraday.physics.utoronto.ca/IYearLab/Intros/StandingWaves/Flash/sta1fix.html • Result • Pressure wave node at end, antinode at other • Pipe length is some odd multiple of ¼ wavelength**Standing waves in Air – open/closed end (3)**• Allowed widths • In general • Allowed wavelengths • ,3,5…. • Allowed frequencies Velocity is**Comparison of waves on string and air**• Both have • Wavelength – distance between peaks at fixed time • Frequency – rate of repetitions at fixed position (like your ear) • Wave velocity • Differences • String wave velocity varies with tension and mass/length • String has ½- wavelength harmonics • Air wave velocity set at 343 m/s (at 20° C) • Air has ½- or ¼- wavelength harmonics**Examples of String and Air Instruments**• String Instruments • Guitar • Violin • Piano • Air Instruments • Flute • “Trombone” • Soda bottle**Examples**• Examples • Problem 25 – Open & closed, 1st 3 harmonics • Problem 26 – Coke bottle • Problem 27 – Range of human hearing, pipe lengths • Problem 28 – Guitar sounds with fret • Problem 29 – Guitar sounds with fret • Problem 30 – Length of organ pipe • Problem 32 – Flute • Problem 34 – Pipe multiple harmonics**Problem 25 – Organ Pipe**• Open at both ends Closed at one end <<skip even harmonics**Problem 26 – Coke bottle**• Open/closed fundamental • Closed 1/3 way up**Problem 27 – Full-range Pipe Organ**• Open/open fundamental • Lowest frequency • Highest frequency**Problem 28 – Guitar**• Original frequency of 3rd harmonic (on string) • Fingered frequency of fundamental • Ratio**Problem 29 – Guitar (1)**• Unfingered frequency of fundamental (on string) • Fingered frequency of fundamental • Ratio**Problem 29 – Guitar (2)**• wavelength of 440 Hz fundamental in string • frequency in air 440 Hz • Wavelength in air different because of air**Problem 30 – Organ Pipe**• Corrected velocity to 21°C • Allowed frequencies • Length is • Wavelength same inside and outside tube**Problem 32 - Flute**• Flute open at both ends (open-open) • Allowed frequencies • Length is**Problem 34 – Assume open-open <?>**• Write n and (n+1) harmonics in terms of fundamental • Subtract • So the difference of any 2 harmonics should be the fundamental. ????!!**Problem 34 – Assume open-closed <?>**• Write n and (n+2) odd harmonics in terms of fundamental • Subtract • So the difference of any 2 harmonics should be twice fundamental. success!!

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