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

Example 12-7

Example 12-8

Longitudinal Waves in Air Traveling sound wave 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 Result: – Pressure wave node at both ends – Pipe length is some multiple of ½ wavelength!

Standing waves in Air – open/open end (3)

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 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)

Comparison of waves on string and air

Examples of String and Air Instruments String Instruments – Guitar – Violin – Piano Air Instruments – Flute – “Trombone” – Soda bottle

Examples – Problem 25 – Open & closed, 1 st 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

Problem 26 – Coke bottle

Problem 27 – Full-range Pipe Organ

Problem 28 – Guitar

Problem 29 – Guitar (1)

Problem 29 – Guitar (2)

Problem 30 – Organ Pipe

Problem 32 - Flute

Problem 34 – Assume open-open

Problem 34 – Assume open-closed