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Questions and Answers
Which of the following equations represents the wave equation for a string under tension?
Which of the following equations represents the wave equation for a string under tension?
- y(x, t) = A cos(kx)cos(ωt)
- y(x, t) = A sin(kx)sin(ωt)
- y(x, t) = A sin(kx)cos(ωt) (correct)
- y(x, t) = A cos(kx)sin(ωt)
What type of wave is formed when two waves of the same frequency and amplitude traveling in opposite directions superpose?
What type of wave is formed when two waves of the same frequency and amplitude traveling in opposite directions superpose?
- Polarized wave
- Longitudinal wave
- Transverse wave
- Standing wave (correct)
What type of wave is formed when two waves of the same frequency and amplitude traveling in opposite directions superpose?
What type of wave is formed when two waves of the same frequency and amplitude traveling in opposite directions superpose?
- Standing wave (correct)
- Longitudinal wave
- Transverse wave
- Progressive wave
What is the characteristic of a stationary wave?
What is the characteristic of a stationary wave?
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What is the characteristic of a stationary wave?
What is the characteristic of a stationary wave?
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Which of the following equations represents the wave equation for a string under tension?
Which of the following equations represents the wave equation for a string under tension?
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Study Notes
Wave Equations and Stationary Waves
- The wave equation for a string under tension is represented by the equation: ∂²u/∂t² = v² ∂²u/∂x²
- When two waves of the same frequency and amplitude traveling in opposite directions superpose, a standing wave (or stationary wave) is formed
- A standing wave is characterized by nodes (points of zero amplitude) and antinodes (points of maximum amplitude)
- Standing waves have fixed nodes and antinodes, and the waveform appears to be standing still, hence the name "standing wave"
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