Waves - Result Question 56

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58. Two identical piano wires kept under the same tension $T$ have a fundamental frequency of 600 $Hz$. The fractional increase in the tension of one of the wires which will lead to occurrence of 6 beats/s when both the wires oscillate together would be

======= ####58. Two identical piano wires kept under the same tension $T$ have a fundamental frequency of 600 $Hz$. The fractional increase in the tension of one of the wires which will lead to occurrence of 6 beats/s when both the wires oscillate together would be

3e0f7ab6f6a50373c3f2dbda6ca2533482a77bed:content/english/neet-pyq-chapterwise/physics/waves/waves—result-question-56.md (a) 0.02

(b) 0.03

(c) 0.04

(d) 0.01

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Answer:

Correct Answer: 58. (a)

Solution:

  1. (a) For fundamental mode, $f=\frac{1}{2 \ell} \sqrt{\frac{T}{m}}$

Taking logarithm on both sides, we get $\Rightarrow \log f=\log (\frac{1}{2 \ell})+\log (\sqrt{\frac{T}{\mu}})$

$\Rightarrow \log (\frac{1}{2 \ell})+\frac{1}{2} \log (\frac{T}{\mu})$

or $\log f=\log (\frac{1}{2 \ell})+\frac{1}{2}[\log T-\log \mu]$

Differentiating both sides, we get

$\frac{df}{f}=\frac{1}{2} \frac{dT}{T}$ (as $\ell$ and $\mu$ are constants)

$\Rightarrow \frac{dT}{T}=2 \times \frac{df}{f}$

Here $df=6$

$f=600 Hz$

$\therefore \frac{dT}{T}=\frac{2 \times 6}{600}=0.02$