KCET · Physics · 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 \(9: 1\)
- B \(1: 9\)
- C \(3: 1\)
- D \(1: 3\)
Answer & Solution
Correct Answer
(A) \(9: 1\)
Step-by-step Solution
Detailed explanation
\(\quad v=\frac{1}{2 l} \sqrt{\frac{\mathrm{T}}{\mathrm{m}}}\)
\(\Rightarrow \quad v \propto \frac{\sqrt{\mathrm{T}}}{1}\)
\(\frac{\mathrm{T}_{2}}{\mathrm{~T}_{1}}=\left[\frac{\mathrm{v}_{2}}{\mathrm{v}_{1}}\right]^{2}\left[\frac{\mathrm{l}_{2}}{\mathrm{l}_{1}}\right]^{2}=\left[\frac{300}{200}\right]^{2}\left[\frac{21}{\mathrm{l}}\right]^{2}=\frac{9}{1}\)
\(\Rightarrow \quad v \propto \frac{\sqrt{\mathrm{T}}}{1}\)
\(\frac{\mathrm{T}_{2}}{\mathrm{~T}_{1}}=\left[\frac{\mathrm{v}_{2}}{\mathrm{v}_{1}}\right]^{2}\left[\frac{\mathrm{l}_{2}}{\mathrm{l}_{1}}\right]^{2}=\left[\frac{300}{200}\right]^{2}\left[\frac{21}{\mathrm{l}}\right]^{2}=\frac{9}{1}\)
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