Standing Waves and Sound Resonance Waves on a

Standing Waves and Sound Resonance Waves on a String, in an openended pipe, and in a closed-ended pipe

Harmonics on a String Warm-up: (assume the string is fixed at both ends) n n n 1 st Harmonic/Fundamental Frequency: 2 nd Harmonic (1 st Overtone): 3 rd Harmonic (2 nd Overtone): 4 th Harmonic (3 rd Overtone): List the equation for wavelength (λ), in terms of the length of the string (L) for EACH of these harmonics. If the string is 1. 20 m long, and f 0 = 28 Hz, determine the frequency that will cause each harmonic, and determine the wavelength of each

Harmonics on a String 1 st Harmonic/Fundamental Frequency Wavelength (λ) = 2 L Frequency = fo

Harmonics on a String n

Closed End Resonance n

Harmonics in a Closed Pipe 3 rd Harmonic 5 th Harmonic 7 th NOTICE: Only odd harmonics are present! n 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 (λ) for each of these?

Harmonics in an Closed Pipe Wavelength (λ) = 4 L

Open End Resonance n

Harmonics in an Open Pipe n 2 nd harmonic Harmonic n 3 rd harmonic 4 th 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 (λ) for each of

Harmonics in an Open Pipe Wavelength (λ) = 2 L Wavelength (λ) = L