COMEDK · Physics · 16. Waves and Sound
A string vibrates with a frequency of \(200 \mathrm{~Hz}\). When its length is doubled and tension is altered, it begins to vibrate with a frequency of \(300 \mathrm{~Hz}\). The ratio of the new tension to the original tension is
- A 3 : 1
- B 9 : 1
- C 1 : 9
- D 1 : 3
Answer & Solution
Correct Answer
(B) 9 : 1
Step-by-step Solution
Detailed explanation
The fundamental frequency of a vibrating string is given by \(f = \dfrac{1}{2L} \sqrt{\dfrac{T}{\mu}}\), where \(L\) is the length, \(T\) is the tension, and \(\mu\) is the linear mass density. Let the initial frequency be \(f_1 = 200 \text{ Hz}\), length be \(L_1 = L\), and…
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