# Standing Waves and Sound Resonance - Physics Rocks! Standing Waves and Sound Resonance Waves on a String, in an open-ended pipe, and in a closed-ended pipe Harmonics on a Warm-up: (assume the string is fixed at String both ends)

1st Harmonic/Fundamental Frequency: 2nd Harmonic (1st Overtone): 3rd Harmonic (2nd Overtone): 4th Harmonic (3rd Overtone): List the equation for wavelength ()), in terms of the length of the string (L) for EACH of these harmonics. If the string is 1.20 m long, and f0 = 28 Hz, determine the frequency that will cause each harmonic, and determine the

Harmonics on a String 1st Harmonic/Fundamental Frequency Wavelength () = 2L )) = 2L Frequency = fo 2nd Harmonic/1st Overtone Wavelength () = 2L )) = Frequency = 2fo 3rd Harmonic/2nd Overtone Wavelength () = 2L )) = Frequency = 3fo 4th Harmonic/3rd Overtone Wavelength () = 2L )) = Frequency = 4fo

Harmonics on a String General Relationship for standing waves on a string: n = harmonic number (1, 2, 3, ) L = length of string Closed End Resonance Closed End Resonator: Any column of air that is closed at one

end only. It is open at the other end Nodes will ALWAYS be found at the closed end Antinodes will ALWAYS be found at the open end At the fundamental frequency: Harmonics in a Closed Pipe 3rd Harmonic

5th Harmonic Harmonic 7th NOTICE: Only odd harmonics are present! Sketch the waveforms that would represent the displacement of the air molecules within the air column. What, in terms of the length of the pipe (L), is the wavelength ()) for each of these? Harmonics in an

Closed Pipe Wavelength () = 2L )) = 4L = Wavelength () = 2L )) = L Wavelength () = 2L )) = L Wavelength () = 2L )) = L Open End Resonance Open End Resonator:

Any column of air that is open at both ends Antinodes will always be found at both ends At the fundamental frequency: Harmonics in an Open Pipe 2nd harmonic

Harmonic 3rd harmonic 4th Sketch the waveforms that would represent the displacement of the air molecules within the air column. What, in terms of the length of the pipe (L), is Harmonics in an Open Pipe Wavelength () = 2L )) = 2L

= Wavelength () = 2L )) = L Wavelength () = 2L )) = L Wavelength () = 2L )) = L