|
1
|
- Harmonic Frequencies
- Open and Closed-pipe resonance
|
|
2
|
- Most objects have a Natural Frequency, which is the frequency at which
they will naturally vibrate.
- If some wave source, like a sound speaker, is placed near an object, the
sound waves from the speaker will transfer energy to it and cause it to
begin vibrating…
- If the frequency of the sound wave is exactly the same as the
object’s natural frequency, standing waves will form in the
object…
|
|
3
|
- Because the wave frequency of the wave source matches the natural
frequency of the object, it will vibrate (oscillate) at a maximum
amplitude
- If the amplitude of the incoming sound wave is increased, then the
amplitude of the standing wave in the object will also increase
- Resonance will also occur at other regular multiples of the natural
frequency…
|
|
4
|
- Fundamental Frequency:
(a.k.a. first harmonic)
- The lowest frequency that will cause a standing wave to form on a
string or in a column of air
- Harmonic Frequencies: (a.k.a. Resonant Frequencies)
- Any frequency that causes a string or a column of air to resonante (a
standing wave is formed)
- Will be some multiple of the fundamental frequency
|
|
5
|
- First Harmonic:
- Second harmonic:
- Third Harmonic:
|
|
6
|
- General Relationship for standing waves on a string:
- n = harmonic number (1, 2, 3, …)
- L = length of string
|
|
7
|
- Open Pipe Resonator:
- Any column of air that is open at Both ends
- Displacement antinodes will
always be found at both ends
- At the fundamental frequency:
|
|
8
|
- 2nd harmonic 3rd
harmonic
4th Harmonic
|
|
9
|
- Closed Pipe Resonator:
- Any column of air that is closed at one end only. It is open at the other end
- Displacement nodes will ALWAYS
- be found at the closed end
- Displacement antinodes will
always be found at the open end
- At the fundamental frequency:
|
|
10
|
- 2nd Harmonic 3rd
Harmonic
4th Harmonic
|
Notes
