4.5 Standing Waves

The diagrams show the structure of a violin and a close-up of the tuning pegs.

The strings are attached at end X then pass over a bridge which acts as a fixed point. The strings are also fixed at the other end, where they are wound around cylindrical spools, fixed to tuning pegs.

Strings for musical instruments create notes according to their tension and a property of the string called mass per unit length, μ. 

The properties of the string and the frequency of the first harmonic are related by the equation:

Where f = frequency of first harmonic (Hz), L = length (m), T = tension (N) and μ = mass per unit length (kg m⁻¹).

The mass of a particular string is 1.4 × 10^–4 kg and it has a vibrating length of 0.35 m. When the tension in the string is 25 N, it vibrates with a first-harmonic frequency of 357 Hz.

The graph shows how the tension in the string varies with the extension of the string. 

The string, under its original tension of 25 N is vibrating at a frequency of 357 Hz. The diameter of the cylindrical spool is 6.50 × 10^–3 m.

The diagram shows a common piece of teaching laboratory equipment which can be used to demonstrate wave phenomena.

The speed of sound in the tube is 340 m s⁻¹ and the frequency of the sound emitted by the loudspeaker is 880 Hz.