MHT CET · Physics · Waves and Sound
When tension 'T' is applied to a sonometer wire of length \(\ell^{\prime}\), it vibrates with the fundamental frequency 'n'. Keeping the experimental setup same, when the tension is increased by 8 newton, the fundamental frequency becomes three times the earlier fundamental frequency (n). The initial tension applied to the wire in newton, was
- A 2
- B 0.5
- C 1
- D 2.5
Answer & Solution
Correct Answer
(C) 1
Step-by-step Solution
Detailed explanation
(C)
\(\mathrm{n}=\frac{1}{2 \ell} \sqrt{\frac{\mathrm{T}}{\mathrm{m}}}\)
\(3 \mathrm{n}=\frac{1}{2 \ell} \sqrt{\frac{\mathrm{T}+8}{\mathrm{~m}}}\)
\(\therefore \frac{\mathrm{n}}{3 \mathrm{n}}=\sqrt{\frac{\mathrm{T}}{\mathrm{T}+8}}\)
\(\frac{\mathrm{n}^{2}}{9 \mathrm{n}^{2}}=\frac{\mathrm{T}}{\mathrm{T}+8}\)
\(\therefore \mathrm{T}+8=9 \mathrm{~T} \Rightarrow 8 \mathrm{~T}=8 \mathrm{~N}\)
\(\therefore 1 \mathrm{~N}\)
\(\mathrm{n}=\frac{1}{2 \ell} \sqrt{\frac{\mathrm{T}}{\mathrm{m}}}\)
\(3 \mathrm{n}=\frac{1}{2 \ell} \sqrt{\frac{\mathrm{T}+8}{\mathrm{~m}}}\)
\(\therefore \frac{\mathrm{n}}{3 \mathrm{n}}=\sqrt{\frac{\mathrm{T}}{\mathrm{T}+8}}\)
\(\frac{\mathrm{n}^{2}}{9 \mathrm{n}^{2}}=\frac{\mathrm{T}}{\mathrm{T}+8}\)
\(\therefore \mathrm{T}+8=9 \mathrm{~T} \Rightarrow 8 \mathrm{~T}=8 \mathrm{~N}\)
\(\therefore 1 \mathrm{~N}\)
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