(a) Explain the term resonance and give two examples (b)(i) Describe, with the aid of a labelled diagram, an experiment to show how the frequency of the not...

(a) Resonance

Resonance is the phenomenon in which a body is forced to vibrate at its natural frequency by a periodic force of the same frequency, producing vibrations of maximum amplitude.

Examples are:

1. tuning a radio receiver to a particular station;
2. a diver's board vibrating strongly when it is periodically forced at its natural frequency.

(b)(i) Experiment to investigate the effect of length on the frequency of a vibrating string

A sonometer wire is stretched over two bridges, A and B, on a hollow wooden box. The wire passes over a smooth pulley and is kept taut by a constant load, W. Bridge B is movable, so that the vibrating length, L, between the bridges can be altered. A light paper rider is placed at the middle of the vibrating length.

A tuning fork of known frequency is struck gently with a rubber bung and its stem is placed on the sonometer box. The movable bridge is adjusted until resonance occurs. Resonance is indicated when the paper rider is thrown off the wire or when the sound becomes loud. The resonating length, L, is measured.

The procedure is repeated with tuning forks of different known frequencies while the load, and hence the tension, is kept constant. The readings may be recorded as follows:

A graph of frequency, f, against reciprocal length, 1/L, is plotted.

The straight line through the origin shows that, for constant tension and the same wire,

\[f \propto \frac{1}{L}.\]

(b)(ii) Precautions

1. Keep the tension constant throughout by using the same load and a smooth pulley.
2. Strike each tuning fork gently on a rubber bung and measure the distance between the inner edges of the bridges without parallax.

(c) For the fundamental mode of a stretched string,

\[f=\frac{1}{2L}\sqrt{\frac{T}{\mu}},\]

where \(T\) is the tension and \(\mu\) is the mass per unit length of the wire.

(i) If \(T\) becomes \(9T\),

\[f'\propto\sqrt{9T}=3\sqrt{T}.\]

Therefore, the fundamental frequency is tripled.

(ii) If the length becomes \(2L\),

\[f'=\frac{1}{2L}f.\]

Therefore, the fundamental frequency is halved.