

Explanation
(a) Resonance occurs whenever a particular body or system is set in oscillation at its own natural frequency as a result of impulses received from some other body or system which is vibrating with the same frequency. At resonance, the amplitude is maximum. Two examples of resonance are tuning a radio and divers board.

Procedure: In the diagram above the string is kept taut by using a constant weight
(w) between the two bridges A and B. The length, L between the bridges is adjusted until the wire resonates with the vibrating tuning fork. This happens when a paper rider flies off or when a loud sound is heard. Then, measure length, L of the resonating wire and frequency f. The experiment is repeated for at least four other tuning forks of known frequencies. In each case the values of the frequency, f and the corresponding length, L are recorded. A graph of f is plotted against 1/L or L against 1/f. A straight-line graph passing through origin is obtained showing that frequency is proportional to the reciprocal of the length.
(iii) Precautions:
(1) A smooth pulley should be used
(2) the tuning fork should be struck on a rubber bung
(c) For a fundamental note
f\(_o\) = \(\frac{1}{20}\) = \(\sqrt{\frac{T}{m}}\)
where f\(_o\) = fundamental frequency
L = Length of string
T = Tension m = linear density or mass per unit length of the string
(i) \(f_1 = \frac{1}{20} \sqrt{\frac{f}{m}}\) = 3(\(\frac{1}{20} \sqrt{\frac{1}{20}} \sqrt{\frac{1}{m}})\)
f\(_1 = 3f_o\)
i.e = the fundamental frequency, \(f_o\) is tripled
(ii) \(f_2 = \frac{1}{20} (\frac{1}{20} \sqrt{\frac{T}{m}}) = \frac{1}{2} \times \frac{1}{20} \sqrt{\frac{1}{m}} = f_2 = \frac{1}{2} f_o\)
i.e the fundamental frequency, \(f_o\) is halved

