Standing waves

Standing Waves

  • Standing waves, also known as stationary waves, differ from travelling waves in that the points of identical phase do not appear to move. Instead, they oscillate in place about their equilibrium position.

  • They are formed as a result of superposition between two waves of the same frequency and amplitude travelling in opposite directions.

  • Nodes and antinodes are characteristic of standing waves. Nodes are locations where the wave particles do not move, i.e., the displacement at a node is always zero. Antinodes are locations where the wave has maximum amplitude; the displacement is highest at these points.

Properties of Standing Waves

  • The wavelength of a standing wave is twice the distance between successive nodes or between successive antinodes.

  • The frequency of a standing wave is the same as the frequency of the waves that create it.

  • The vibrational modes of a standing wave represent distinct patterns in which the wave can vibrate. Each mode corresponds to a distinct frequency, and these frequencies are often referred to as harmonic frequencies or simply harmonics.

Energy and Standing Waves

  • In standing waves, energy is not transported from one end of the wave to the other as in travelling waves.

  • The energy of a standing wave is mainly concentrated around the antinodes where the amplitude of vibration is the greatest.

  • Energy is not consumed or transmitted in a standing wave; rather, it is continually transferred back and forth from potential energy of the particles displaced from their equilibrium to the kinetic energy of each vibrating particle.

Phenomena Involving Standing Waves

  • Many musical instruments produce sound using standing waves. The principles of standing waves are utilised to manipulate and control the frequencies of sound produced.

  • Resonance is closely associated with standing waves. When a system is forced to vibrate at its natural frequency, a high amplitude standing wave is established, which is resonance.

  • In destructive resonance, certain frequencies can produce standing waves that result in large vibrations and can cause damage to the system. Examples of this include shattering of glass when exposed to a particular sound frequency.