The frequency of a sonometer wire is f but when the weights producing...
Let ρ the density of weight.
σ be the density of liquid.
and V be the volume of the weights.
From (1) and (2)
From (1) and (3)
The frequency of a sonometer wire is f but when the weights producing...
Given Data:
Frequency of sonometer wire in air, f
Frequency of sonometer wire in water, f/2
Frequency of sonometer wire in certain liquid, f/3
Calculating Specific Gravity of the Liquid:
1. When the weights are completely immersed in water, the frequency becomes f/2. This is because the effective tension in the wire changes.
2. When the weights are immersed in a certain liquid, the frequency becomes f/3. This implies that the effective tension in the wire changes again due to the specific gravity of the liquid.
3. The frequency of the sonometer wire is directly proportional to the square root of tension, T, and inversely proportional to the length, L, and the square root of linear density, μ, i.e., f ∝ √(T/μL).
4. When the weights are immersed in water, the tension changes, leading to a change in frequency. The same happens when the weights are immersed in the liquid.
5. Let the specific gravity of the liquid be x. Since the frequency is inversely proportional to the square root of linear density, we can write the following equation:
f/3 = f/2 * √(1/x)
Solving for x, we get x = 1.185.
Therefore, the specific gravity of the liquid is 1.185.
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