Standing waves/beats/timbre- explanations

Difference between a travelling wave and a standing wave? (Energy, Amplitude, Wave source, Interference)

Energy: travelling waves transfer energy where are standing waves don’t

Amplitude: The amplitude is the same at different places on a travelling wave. The amplitude is different at different places on a standing wave

Wave source: travelling waves have one source but a standing wave requires 2 sources- the reflected wave that interferes or superimposes on the initial incoming wave.

Interference: Standing waves require interference but travelling waves do not. Interference forms nodes and antipodes in a standing wave.

What conditions are needed to form a standing wave

• a standing wave requires waves with the same frequency and amplitude to superimpose (interfere)

• Standing waves have to ‘fit’ in the string or pipe

• The string length is a multiple, of the wave length

How does a travelling wave form a standing wave in a string?

• Standing waves form when the incident wave and the inverted reflected wave interfere (superimpose). The reflections interfere and produce a standing wave with a frequency that is the natural or resonant frequency of the string.

• Nodes are caused by destructive interference where the waves are in opposite phase (180 out of phase) and occur at the fixed end of the string

• Antinodes are formed by constructive interference where waves are in phase

• Only wave lengths that ‘fit’ the string (nodes at both ends) will resonate and produce a standing wave with nodes and antinodes

how does a standing wave form in a pipe?

• air is blown down the pipe, producing vibrations of sound that travel down the length of the pipe

• Standing waves form when the incident wave and the reflected wave interfere (superimpose). The reflections interfere and produce a standing wave with a frequency that is natural or resonant frequency of the pipe.

• Nodes are caused by destructive interference where the waves are in opposite phase (180 out of phase). This occurs at the end of a pipe.

• Antinodes are formed by constructive interference where waves are in phase. This occurs at the open end of a pipe where the reflected wave is still in phase

• Only wave lengths that ‘fit’ the pipe (eg antinodes at both ends for an open pipe) will resonate and produce a standing wave with nodes and antinodes

why open/closed pipe only has odd numbered harmonics?

A pipe open at one end and closed at the other must have a displacement antinode at the open end and a displacement node at the closed end. The tube/pipe will only fit in an odd number harmonics (the fundamental frequency multiplied by 1,3,5…) as the tube ‘fits’ only an odd number of wavelengths

beats definition

The pulsating loud and soft sound produced when two waves of slightly different frequencies interfere. The 2 waves superimpose, where the waves amplitudes add together (constructive interference) the sound is loud, where the waves amplitudes cancel (deconstructive interference) the sound is quiet. The sound pulsates with a beat frequency fb=f1-f2. The closer the two beat frequencies the lower will be the beat frequency until this becomes zero when they are perfectly in tune.

Timbre

• the Timbre or difference in a note is determined by the combination of the fundamental and its overtones (harmonics)

• The overtones in different instruments differ in number or strength so the resultant wave for is different for each instrument.