Physics
Physics
Problem
In a sonometer wire, the tension is maintained by suspending a 50.7 kg mass from the free end of the wire. The suspended mass has a volume of . The fundamental frequency of vibration of the wire is 260 Hz. If the suspended mass is completely submerged in water, the fundamental frequency will become ..... Hz.Intuitive explanation
The key insight is that submerging the mass in water reduces the effective tension in the wire through buoyancy—the water exerts an upward force that partially counteracts gravity. Since the fundamental frequency of a vibrating string depends on (where is tension), you need to find how the tension changes when buoyancy acts, then use that ratio to find the new frequency. The mass and wire properties stay the same; only the downward force changes.
Intuitive explanation
The key insight is that submerging the mass in water reduces the effective tension in the wire through buoyancy—the water exerts an upward force that partially counteracts gravity. Since the fundamental frequency of a vibrating string depends on (where is tension), you need to find how the tension changes when buoyancy acts, then use that ratio to find the new frequency. The mass and wire properties stay the same; only the downward force changes.