1. Resonance And you

2. Resonance Small periodic oscillations produce large amplitude oscillations Swing example – add E at just the right time = larger amplitude oscillations

3. Acoustic resonance The tendency of an acoustic system to absorb more energy when it is driven at a frequency that matches one of its own natural frequencies of vibration. http://www.youtube.com/watch?v=17tqXgv CN0E http://www.youtube.com/watch?v=17tqXgv CN0E Acoustics is the study of mechanical waves in solids, liquids, and gases.

4. An acoustically resonant object usually has more than one resonance frequency, especially at harmonics of the strongest resonance. Recall that harmonics refers to the harmonious sounds produced by wave interactions (interference patterns) of waves that have lengths that are whole number ratios. An octave is a 2:1 ratio, a fifth is a 3:2 ratio

5. Closed end tubes Wind instruments have resonant frequencies that correspond to the length of the tube. The fundamental frequency is the most basic wave form that will produce a resonant frequency in the tube (the the fundamental frequency of the slinky) Qualifier: the antinode will be present at the open end and the node at the closed end

6. Do you recall That with the string, the relationship of the Length to the wavelength was: L = n/2 λ where n = the 1 st, 2 nd, 3 rd,... fundamental n = 3 n=2 n=1

7. Well The same type of relationship exists for tubes. Here a closed end tube produces standing waves like this: Note the node is at the closed end and the antinode is at the open end

8. So to describe the standing wave in the pipe, I will use a transverse wave graphic even though the sound wave is a longitudinal wave n = 1 2 3 4 5 6 7 8 9 10 11 n = 1 = fundamental = (¼) ( λ) Therefore: L = (n/4) (λ) where n = odd number integer So: L = ((2n-1)/4) (λ)

9. Challenge problem Derive a relationship that defines the frequency in terms of n, the velocity of the wave, and the length of the tube. Hint: λ = v / f And recall: L = ((2n-1)/4) (λ)

10. Did you find: f n = (2n – 1) (v) / 4L ???? That was epic!!!! So now try to define the same relationship for a string!!!!!!!!!!!!!!!!!!!! Hint: for a string the first fundamental = (½)(λ) So we can state: L = (n/2) (λ) GO!!!

11. Did you say For a string you can define the frequency in terms of the n, v, and L as: f = vn / 2L ???? Bloody well done then!!!!!!!!!!!!!!!!

12. Show pHET site on waves and interference patterns