Final answer:
Changing the effective tension on a sonometer wire alters its fundamental frequency. The new tension is calculated by accounting for the buoyant force, and the new frequency is determined from the relationship between tension and frequency. The change in mass due to immersion in a liquid with a different density affects the overall tension, leading to a change in frequency.
Step-by-step explanation:
The question concerns the change in the fundamental frequency of a sonometer wire when the tension is altered. In the problem, the mass originally causing the tension is immersed in a liquid, changing the effective tension due to the buoyant force. Since the tension in the wire is related to the square of the frequency (f = (1/2L) * sqrt(T/μ)), where L is the length of the wire, T is the tension in the wire, and μ is the linear mass density, any change in tension will affect the frequency.
When the block is immersed in the liquid, its effective weight (and therefore the tension in the wire) is decreased because of the buoyant force provided by the liquid. The buoyant force is equal to the weight of the liquid displaced by the block, which can be calculated using the density of the liquid and the volume of the immersed block.
The new tension, T', is calculated using T' = T - V * (ρliquid - ρair) * g, where V is the volume of the block and g is the acceleration due to gravity. With this new tension, you can solve for the new frequency using the modified equation for f.