Physics
Textbooks
Boundless Physics
Sound
Further Topics
Physics Textbooks Boundless Physics Sound Further Topics
Physics Textbooks Boundless Physics Sound
Physics Textbooks Boundless Physics
Physics Textbooks
Physics
Concept Version 9
Created by Boundless

Standing Waves on a String

Standing wave occurs due to the interference when transverse waves in strings are reflected and the incident and reflected waves meet.

Learning Objective

  • Identify when a standing wave occurs


Key Points

    • The reflected wave is inverted from the incident wave when a transverse wave on a string is fixed at the end point. The reflected wave is not inverted from the incident wave when a transverse wave on a string is free at the end point.
    • A standing wave occurs when an incident wave meets a reflected wave on a string.
    • A standing wave contains nodes (points that remain flat due to the destructive interference) and antinodes (points with maximum oscillation due to the constructive interference).
    • Every point in the string oscillates up and down and the amplitude of the oscillations depends on the location of the point.
    • A standing wave has some points that remain flat due to destructive interference. These are called antinodes.
    • The points on a standing wave that have reached maximum oscillation do so from constructive interference, and are called nodes.

Terms

  • transverse wave

    Any wave in which the direction of disturbance is perpendicular to the direction of travel.

  • destructive interference

    Occurs when waves interfere with each other crest to trough (peak to valley) and are exactly out of phase with each other.

  • constructive interference

    Occurs when waves interfere with each other crest to crest and the waves are exactly in phase with each other.


Example

    • Think about how a guitar works. When you pluck a string, it appears to vibrate. This vibration is just a very small standing wave. For the most part, the frequency of this wave will remain constant. Since frequency characterizes the pitch, the sound is a constant note. This is the basis not only for a guitar, but any other string instrument.

Full Text

A standing wave is a wave that appears stationary, meaning it remains in a constant position. In a string, a standing wave is a type of transverse wave—where the movement of the particles of the medium is perpendicular to the direction of the propagation of the wave. A standing wave can occur when two identical waves moving in different directions along the string interfere.

There are two scenarios of waves in strings: the string is fixed at both ends, or the string is fixed at one end and free at the other. A transverse wave will move along the string until it reaches the other end. It is then reflected from that end and starts to move back towards the original direction; at this point interference occurs. shows a transverse wave that is reflected from a fixed end. When a transverse wave meets a fixed end, the wave is reflected, but inverted. This swaps the peaks with the troughs and the troughs with the peaks. diagrams a transverse wave on a string that meets a free end. The wave is reflected, but unlike a transverse wave with a fixed end, it is not inverted.

Free End Reflection

The wave is reflected, but unlike a transverse wave with a fixed end, it is not inverted.

Fixed End Reflection

When a transverse wave meets a fixed end, the wave is reflected, but inverted.

Standing Waves

When either of the two scenarios of wave reflection occurs, the incident wave meets the reflected wave. These waves move past each other in opposite directions, causing interference. When these two waves have the same frequency, the product of this is called the standing waves. Standing waves appear to be standing still, hence the name. illustrates a very slow moving standing wave. (One application of the principle of standing waves is in music with the concept of resonance—and how many musical instruments, like guitars and pianos, get their sound. ) Let us now examine how standing waves occur.

Standing Wave on a String

This is what a standing wave would look like if you were to slow it down. The wave is caused by an incident wave on a string being reflected and then traveling back in the direction it came from. The two waves then meet and interfere with each other causing this phenomenon.

Constructive vs. Destructive Interference

When the incident wave and reflected wave first meet, both waves have an amplitude is zero. As the waves continue to move past each other they continue to interfere with each other, either constructively of destructively. As discussed in previous atoms, when waves are completely in phase and interfere with each other constructively they are amplified, and when they are completely out of phase and interfere destructively they cancel out. As the waves continue to move past each other, and are reflected from the opposite end, they continue to interfere both ways; a standing wave is produced. Every point in the medium containing a standing wave oscillates up and down, and the amplitude of the oscillations depends on the location of the point. When we observe a standing wave on strings, it appears the wave is not moving but standing still. In summary:

  • The points which reach the maximum oscillation height are called antinodes, and are results of complete constructive interference.
  • The points in a standing wave that appear to remain flat and do not move are called nodes. These are due to complete destructive interference.
[ edit ]
Edit this content
Prev Concept
Spherical and Plane Waves
Standing Waves in Air Columns
Next Concept
Subjects
  • Accounting
  • Algebra
  • Art History
  • Biology
  • Business
  • Calculus
  • Chemistry
  • Communications
  • Economics
  • Finance
  • Management
  • Marketing
  • Microbiology
  • Physics
  • Physiology
  • Political Science
  • Psychology
  • Sociology
  • Statistics
  • U.S. History
  • World History
  • Writing

Except where noted, content and user contributions on this site are licensed under CC BY-SA 4.0 with attribution required.