$(A)$ The number of nodes is $5$ .
$(B)$ The length of the string is $0.25 \ m$.
$(C)$ The maximum displacement of the midpoint of the string its equilibrium position is $0.01 \ m$.
$(D)$ The fundamental frequency is $100 \ Hz$.

$(A)$ the intensity of the sound heard at the first resonance was more than that at the second resonance
$(B)$ the prongs of the tuning fork were kept in a horizontal plane above the resonance tube
$(C)$ the amplitude of vibration of the ends of the prongs is typically around $1 \mathrm{~cm}$
$(D)$ the length of the air-column at the first resonance was somewhat shorter than $1 / 4$ th of the wavelength of the sound in air

$(A)$ With a node at $O$, the minimum frequency of vibration of the composite string is $v_0$
$(B)$ With an antinode at $O$, the minimum frequency of vibration of the composite string is $2 v_0$
$(C)$ When the composite string vibrates at the minimum frequency with a node at $O$, it has $6$ nodes, including the end nodes
$(D)$ No vibrational mode with an antinode at $O$ is possible for the composite string