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AS & A-Level Physics 08 — Superposition, Interference and Diffraction

AS & A-Level Physics 08 — Superposition, Interference and Diffraction

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Independent Deckloop revision aligned with the Cambridge International AS & A Level Physics (9702) syllabus, 2025–2027. Not affiliated with or endorsed by Cambridge International Education. Chapter 8 of 26: Superposition, interference and diffraction. Concepts, worked applications and misconception checks.

Physics EN AS & A-Level
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Demonstrating Stationary Waves

Stationary waves, or standing waves, are formed from the superposition of two identical progressive waves travelling in opposite directions. This can be demonstrated in various systems. With microwaves, a transmitter emits waves towards a metal plate, which reflects them. A detector moved between the transmitter and plate will find points of maximum and minimum signal. On a stretched string, a mechanical vibrator at one end sends waves that reflect from a fixed end. At specific 'resonant' frequencies, a clear pattern of stationary waves appears. In an air column, such as a tube partially submerged in water, a sound source like a tuning fork is held at the open end. The sound waves reflect from the water surface. By adjusting the length of the air column, resonance can be achieved, making the sound much louder and setting up a stationary wave within the tube. In all cases, the key elements are a wave source, a medium, and a reflector.

Key points

  • Stationary waves are formed by the superposition of two identical waves travelling in opposite directions.
  • Microwave setup: a transmitter, a metal reflector, and a movable probe detector.
  • Stretched string setup: a string under tension, a vibrator (signal generator), and a fixed end.
  • Air column setup: a tube with one closed end (e.g., water surface), and a sound source (e.g., tuning fork) at the open end.

Worked example

Question

A student sets up a stationary wave on a stretched string using a vibrator. They find the first harmonic (fundamental frequency) at 50 Hz. What is the lowest frequency above 50 Hz at which another stationary wave pattern will be observed?

Solution

1. Recall that for a stretched string fixed at both ends, stationary waves only form at specific resonant frequencies called harmonics.
2. The harmonics are integer multiples of the fundamental frequency (fn=nf1f_n = n f_1).
3. The first harmonic is f1=50f_1 = 50 Hz (given).
4. The next possible stationary wave is the second harmonic (n=2n=2).
5. Calculate the frequency of the second harmonic: f2=2×f1=2×50 Hz=100f_2 = 2 \times f_1 = 2 \times 50 \text{ Hz} = 100 Hz.

The next lowest frequency is 100 Hz.

Common pitfalls

  • Confusing the properties of stationary and progressive waves. Stationary waves do not transfer energy along the medium, whereas progressive waves do.
  • Assuming any frequency will produce a stationary wave. Clear, large-amplitude stationary waves only form at specific resonant frequencies (harmonics) determined by the boundary conditions of the system.

Prerequisites

  • Stationary waves are a direct result of the principle of superposition.
  • Requires knowledge of wave reflection and basic wave properties like frequency.
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