Advanced Waves: Coherence, Standing Waves, and Polarization
Coherence in Waves
Coherence occurs when two waves maintain a constant phase relationship, essential for creating stable interference patterns.
Standing Waves
Standing waves are formed when two identical waves traveling in opposite directions interfere.
Key Features:
- Nodes: Points of no displacement.
- Antinodes: Points of maximum displacement.
Formula for String or Pipe:
\[
f_n = \frac{nv}{2L}
\]
Where:
- \( n \): Harmonic number.
- \( v \): Wave speed (\( \text{m/s} \)).
- \( L \): Length of the string/pipe (\( \text{m} \)).
Polarization
Polarization restricts light waves to oscillate in a single plane.
Applications:
- Sunglasses reduce glare by blocking polarized light.
- Polarization in communication ensures signal clarity.
Applications of Advanced Waves
Musical Instruments
Standing waves determine pitch and harmonics.
Telecommunications
Polarized signals enhance efficiency in optical fibers.
Scientific Research
Coherence and polarization are vital in spectroscopy and microscopy.
Example Problem
A string \( 2 \, \text{m} \) long produces a standing wave at its second harmonic. If the wave speed is \( 100 \, \text{m/s} \), calculate the frequency.
- Formula:
\[
f_n = \frac{nv}{2L}
\]
- Substitute Values:
\[
f_2 = \frac{2 \cdot 100}{2 \cdot 2} = 50 \, \text{Hz}
\]
Practice Questions
- A string \( 1.5 \, \text{m} \) long vibrates at its third harmonic with a speed of \( 60 \, \text{m/s} \). Calculate the frequency.
- Explain how coherence is crucial in creating laser beams.
- Describe one application of polarization in everyday life.
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