Unit 2 Section 3 Stationary Waves

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What is a Stationary Wave?

Stationary Wave: A wave created by the superposition of two progressive waves with the same frequency and amplitude, moving in opposite directions. No energy is transmitted by a stationary wave.

Resonant frequency: A frequency at which a stationary wave is formed because an exact number of waves are produced in the time it takes for a wave to get to the end of the vibrating medium and back again. At resonant frequencies, an exact number of half wavelengths fit onto the string.

  • You can demonstrate stationary waves by setting up a driving oscillator at one end of a stretched string with the other end fixed. The wave generated is reflected back and forth.
  • If at the right frequency, the oscillator will produce the exact number of waves in the time it takes for a wave to get to the end and back again.
  • The original and reflected waves reinforce each other.
  • These stationary waves are transverse, each particle vibrates at right angles to the string.

A stationary wave is the superposition of two progressive waves, just two waves interfering:

  • At a node, there is total destructive interference - the displacement of the two waves always cancel each other out.
  • At an antinode, there is constructive interference - the displacement of the two waves combine to make a bigger displacement.
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Resonant Frequencies

Fundemental frequency: The lowest possible resonant frequency a stationary wave vibrates at. One loop with a node at each end. One half wavelength fits on the string, so the wavelength is double the length of the string.

Second harmonic: Is a resonant frequency twice the fundemental frequency. There are two loops with a node in the middle and one at each end. Two half wavelengths fit on the string so the wavelength is the length of the string.

Third harmonic: Is a resonant frequency three times the fundemental frequency, 1 and 1/2 wavelengths fit on the string.

  • The longer the string, the lower the fundemental frequency because the half-wavelength is longer (c = f x landa, so if landa increases, f decreases for a fixed c).
  • The heavier the string, the lower the fundemental frequency - because waves travel more slowly down the string. For a given length a lower velocity, c, makes a lower frequency.
  • The looser the string the lower the fundemental frequency - again because waves travel more slowly down a loose string.
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