The diagrams given below show two sound boxes A and B with wires of same length (l) and tension (10 kgf) but different cross-sectional areas. Simultaneously, vibrating tuning forks of frequency 300 Hz are placed on the boxes A and B. The paper rider falls off in case of B but not in case of A.

(a) Name and explain the phenomenon responsible for the falling off of the paper rider in B.

(b) The wire A resonates with a tuning fork of frequency ‘f’. Is ‘f’ greater than, less than or equal to 300 Hz? Justify your answer.

(a) The phenomenon responsible for falling off the paper rider is resonance.
Resonance is a special case of forced vibrations. When the frequency of the externally applied periodic force on a body is equal to its natural frequency, the body readily begins to vibrate with an increased amplitude. This phenomenon is known as resonance.

(b) A thicker wire will vibrate at a lower resonant frequency than a thinner wire if the length, tension, and material are unchanged. This is because the thicker wire has greater mass per unit length, which lowers its natural frequency of vibration. Therefore, the frequency will be less than 300 Hz.