MHT CET · Physics · Waves and Sound
Two identical strings of length ' \(\ell\) ' and '2 \(\ell\) ' vibrate with fundamental frequencies 'N' hertz and '1:5 N' hertz, respectively. The ratio of tensions for smaller length to larger length is
- A 9:1
- B 3:1
- C 1:9
- D 1:3
Answer & Solution
Correct Answer
(C) 1:9
Step-by-step Solution
Detailed explanation
\(\mathrm{N}=\frac{1}{2 \ell} \sqrt{\frac{\mathrm{T}_{1}}{\mathrm{~m}}}\)
\(1.5 \mathrm{~N}=\frac{1}{4 \ell} \sqrt{\frac{\mathrm{T}_{2}}{\mathrm{~m}}}\)
\(\therefore \sqrt{\frac{\mathrm{T}_{1}}{\mathrm{~T}_{2}}}=\frac{\mathrm{N} \times 2 \ell}{1.5 \mathrm{~N} \times 4 \ell}=\frac{1}{3}\)
\(\frac{\mathrm{T}_{1}}{\mathrm{~T}_{2}}=\frac{1}{9}\)
\(1.5 \mathrm{~N}=\frac{1}{4 \ell} \sqrt{\frac{\mathrm{T}_{2}}{\mathrm{~m}}}\)
\(\therefore \sqrt{\frac{\mathrm{T}_{1}}{\mathrm{~T}_{2}}}=\frac{\mathrm{N} \times 2 \ell}{1.5 \mathrm{~N} \times 4 \ell}=\frac{1}{3}\)
\(\frac{\mathrm{T}_{1}}{\mathrm{~T}_{2}}=\frac{1}{9}\)
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