A sonometer wire is vibrating at frequency fo. If the tension in the wire is doubted while the length and the mass per unit length are kept constant, the ne...
Question 1 Report
A sonometer wire is vibrating at frequency fo. If the tension in the wire is doubted while the length and the mass per unit length are kept constant, the new frequency of vibration is
Answer Details
When the tension in a sonometer wire is doubled while the length and the mass per unit length are kept constant, the new frequency of vibration is:
f = (1/2L) * √(T/μ)
Where:
- f is the frequency of vibration
- L is the length of the wire
- T is the tension in the wire
- μ is the mass per unit length of the wire
Since the length and mass per unit length of the wire are kept constant, we can simplify the equation as follows:
f2 = (1/2L) * √(2T/μ)
where f2 is the new frequency of vibration after doubling the tension.
Dividing the new frequency by the original frequency gives:
f2/f0 = √(2T/μ) / √T/μ) = √2
Therefore, the new frequency of vibration is equal to the square root of two times the original frequency:
f2 = f0√2
So the answer is:
- f0√2
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