Two wires A and B of the same material and length are fixed to a wooden board and stretched under the same tension. The cross-sectional area of wire A is greater than that of wire B. When set into vibration using identical tuning forks of frequency 300 Hz, only wire B produces a loud sound.
(a) Name and explain the phenomenon responsible for the loud sound produced by wire B.
(b) A loud sound is heard from wire A when the experiment is repeated using a tuning fork of frequency f. Is 'f' greater than, less than or equal to 300 Hz? Justify your answer.
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(a) The phenomenon is resonance.
The vibrating tuning fork applies an external periodic force of frequency 300 Hz on both the wires, so both of them execute forced vibrations. The natural frequency of wire B happens to be exactly equal to 300 Hz, so wire B vibrates with a very large amplitude and sends out a large amount of energy into the surrounding air. Hence a loud sound is heard from wire B only.
(b) f < 300 Hz
Reason — For wires of the same material, same length and under the same tension, a thicker wire has a greater mass per unit length and therefore a lower natural frequency of vibration. Since wire A is thicker than wire B, the natural frequency of A is less than that of B, i.e., less than 300 Hz.
A loud sound will be heard from wire A only when the frequency of the tuning fork is equal to the natural frequency of A, so that resonance occurs.
Hence, f is less than 300 Hz.