Standing waves and resonance

Learning objectives

Explain the formation of a standing wave by the superposition of two identical waves travelling in opposite directions, and distinguish it from a travelling wave in terms of energy transfer, amplitude and the phase of the particles

Identify nodes and antinodes on a standing wave, and relate the separation of adjacent nodes to half a wavelength

Determine the wavelength and frequency of the fundamental and of higher harmonics for a string fixed at both ends, for a pipe open at both ends and for a pipe closed at one end

Distinguish free from forced oscillations, and explain resonance as the large-amplitude response that occurs when the driving frequency is close to the natural frequency of the system

Describe light, critical and heavy damping, and explain how increasing the damping lowers and broadens the resonance peak and shifts it to a slightly lower frequency

Discuss situations in which resonance is exploited, such as musical instruments, and situations in which it must be avoided, such as buildings during an earthquake, relating each to the degree of damping designed into the system