Principle of Superposition, Interference and Beats: Practice Problem & Solution
Two identical piano wires, kept under the same tension $T$ have a fundamental frequency of $600 \text{ Hz}$. The fractional increase in the tension of one of the wires which will lead to occurrence of $6 \text{ beats/s}$ when both the wires oscillate together would be: (2011 Mains)
Solution Explained:
To solve this problem, we apply the core principles of Principle of Superposition, Interference and Beats. Understanding the underlying formula is key to arriving at the correct answer below:
Fundamental frequency $$f = \frac{1}{2L} \sqrt{\frac{T}{\mu}}$$. Fractional change is $$\frac{\Delta f}{f} = \frac{1}{2} \frac{\Delta T}{T}$$. Given $\Delta f = 6$ and $f = 600$, we have $$\frac{\Delta T}{T} = 2 \times \frac{6}{600} = 0.02$$.
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