SATHEE: Waves - Result Question 56

Waves - Result Question 56

58. Two identical piano wires kept under the same tension $T$ have a fundamental frequency of 600 $H z$ . 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

(a) 0.02

(b) 0.03

(d) 0.01

[2011M]

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Answer:

Correct Answer: 58. (a)

Solution:

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

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

$\Rightarrow \log (\frac{1}{2 ℓ}) + \frac{1}{2} \log (\frac{T}{μ})$

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

Differentiating both sides, we get

$\frac{d f}{f} = \frac{1}{2} \frac{d T}{T}$ (as $ℓ$ and $μ$ are constants)

$\Rightarrow \frac{d T}{T} = 2 \times \frac{d f}{f}$

Here $d f = 6$

$f = 600 H z$

$∴ \frac{d T}{T} = \frac{2 \times 6}{600} = 0.02$

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Waves - Result Question 56

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

Answer:

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58. Two identical piano wires kept under the same tension $T$ have a fundamental frequency of 600 $H z$ . 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