Standing waves review A standing wave occurs when there is constructive interference between a wave and it reflections from a boundary.

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Presentation transcript:

Standing waves review A standing wave occurs when there is constructive interference between a wave and it reflections from a boundary.

Resonance Resonance occurs when the frequency of a periodic force matches the natural frequency of a system. This is a unique behavior of harmonics motion. Music: If you want a musical instrument to have a frequency of 100 Hz to produce a certain sound, you need to create something to produces a natural vibration of 100 Hz. FM radio: when you change stations all you are doing is changing the frequency of the car receiver to match the frequency of a certain station. (FM stands for Frequency modulation)

Fundamental harmonic How many? Nodes: Antinodes: At different frequencies, different standing wave patterns appear on a vibrating string. The lowest frequency and longest wavelength is called the fundamental wave. How many? Nodes: Antinodes:

Second Harmonic How many? Nodes: Antinodes: The next higher frequency wave is the second harmonic wave. Twice the frequency of the fundamental. How many? Nodes: Antinodes:

The third harmonic How many? Nodes: Antinodes: The third harmonic has three times the frequency of the fundamental. How many? Nodes: Antinodes:

How to solve for harmonics 1. Look for the given frequency of the harmonics. 2. Whatever the 1st harmonic is, you will multiply it by the # harmonic you are looking for Ex. What is the 2nd – 5th harmonic when the fist harmonics has a frequency of 7 Hz? Harmonic Frequency 1st 7x1 = 7 2nd 7x2 = 14 3rd 7x3 = 21 4th 7x4= 28 5th 7x5= 35

Example A slinky produces standing waves. The 1st harmonic has a frequency of 12 Hz. Find the 1st – 4th Harmonics. Also what is the 56th Harmonic? Harmonic Frequency 1st 2nd 3rd 4th 56th