A standing wave, also known as a stationary wave, is made up of two waves that have the same amplitude and frequency but are travelling in opposing directions.
There are two types of stationary waves:
(1) transverse waves created by superposing two identical transverse waves going in opposing directions. (2) Longitudinal waves are produced by superpositioning two identical longitudinal waves flowing in opposing directions.
Standing waves, unlike moving waves, do not result in a net energy transmission (because the two waves which make them up are carrying equal energy in opposite directions). It’s worth noting that the particles near the standing wave’s edge do not move. Displacement nodes are points like this.
The name “stationary wave” comes from the fact that the wave velocity is zero. Individual particles are moving, while the stationary wave as a whole is in the same phase. They’re made up of two similar waves travelling in opposite directions superimposed on top of each other.
Table of Contents
Properties of Stationary Waves
- (i) The disturbance is confined to a particular region and there is no onward motion.
- (ii) There is no transference of energy in the medium.
- (iii) The amplitude of vibration of the particles changes from zero (at nodes) to maximum (at antinodes).
- (iv) The particles of the medium at nodes are permanently at rest.
Important Points
| Stationary Waves | Details | Relevant Formulas |
|---|---|---|
| Definition | A type of wave that appears to be stationary in space and is formed by the interference of two waves that are moving in opposite directions. | – |
| Examples | Vibrating guitar strings, sound waves in a closed organ pipe, electromagnetic waves in a waveguide. | – |
| Types | Standing longitudinal waves; Standing transverse waves. | λn = 2L/n (for standing longitudinal waves), λn = 2L/n (for standing transverse waves), where λn is the wavelength of the nth harmonic, L is the length of the medium, and n is the harmonic number. |
Daily Life Examples of Stationary Waves
- Stringed musical instruments, such as guitars, violins, and cellos, produce sound using stationary waves in the strings.
- Wind instruments, such as flutes and clarinets, produce sound using stationary waves in the air column inside the instrument.
- Organ pipes use stationary waves of sound to produce different pitches and tones.
- Microwave ovens use stationary waves of electromagnetic radiation to heat food.
- Radio broadcasting and television transmission use stationary electromagnetic waves to transmit information.
- Fibre optic cables use stationary waves of light to transmit information over long distances.
- Seismic waves during earthquakes produce stationary waves in the earth’s crust.
- Vibrating strings in musical instruments, such as harps, pianos, and harpsichords, produce stationary waves that create different notes.
- X-rays used in medical imaging produce stationary waves of electromagnetic radiation.
- Resonance tubes in physics labs use stationary waves of sound to measure the speed of sound in air.
Summary
- Stationary waves are formed when two waves of equal amplitude and frequency interfere with each other while moving in opposite directions.
- These waves create a unique pattern of nodes and antinodes that appear to be standing still.
- Stationary waves can occur in a variety of systems including strings, air columns, and electromagnetic waves.
- They have multiple frequencies that are related to the fundamental frequency and the length of the medium.
- Stationary waves are important in many areas of physics and engineering, including acoustics, optics, and telecommunications.
Solved Numerical Problem
A string of length 60cm is fixed at both ends. If the string vibrates in its first harmonic with a wavelength of 120cm, how many antinodes and nodes are there in the string?
Solution:
For a stationary wave in its first harmonic, the string has one antinode in the middle and two nodes at the ends.
Since the wavelength is twice the distance between two adjacent nodes, we can find the number of nodes by dividing the length of the string by the wavelength:
Number of nodes = Length of string / Wavelength
Number of nodes = 60cm / 120cm = 0.5
However, we know that the number of nodes must be an integer, so we need to round this value up or down. Since we have two nodes at the ends of the string, we know that there must be an even number of nodes, so we’ll round the value of 0.5 up to 2.
Therefore, there are two nodes and one antinode in the string.
Multiple Choice Questions
- What are stationary waves?
A. Waves that travel through space and time
B. Waves that are formed by the interference of two waves that are moving in opposite directions
C. Waves that can only be observed in a laboratory setting
D. Waves that always have a constant frequency
Answer: B
- Which of the following is an example of a stationary wave?
A. A person shouting in a quiet room
B. Ripples on the surface of a pond
C. A radio signal transmitted from a tower
D. A guitar string vibrating after being plucked
Answer: D
- What determines the pitch of a note produced by a vibrating guitar string?
A. The frequency of the wave travelling through the string
B. The amplitude of the wave travelling through the string
C. The interference pattern created by the wave reflecting off the ends of the string
D. The standing wave pattern created by the interference of two waves travelling in opposite directions
Answer: D
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