SATHEE: Wave Motion 2 Question 20

Wave Motion 2 Question 20

20. Two vibrating strings of the same material but of lengths $L$ and $2 L$ have radii $2 r$ and $r$ respectively. They are stretched under the same tension. Both the strings vibrate in their fundamental modes. The one of length $L$ with frequency $v_{1}$ and the other with frequency $v_{2}$ . The ratio $v_{1} / v_{2}$ is given by

(2000, 2M)

(a) 2

(b) 4

(d) 1

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Answer:

Correct Answer: 20. (d)

Solution:

Fundamental frequency is given by

$v = \frac{1}{2 l} \sqrt{\frac{T}{μ}}$

(with both the ends fixed)

$∴$ Fundamental frequency

$v \propto \frac{1}{l \sqrt{μ}} (for same tension in both strings)$

where, $μ =$ mass per unit length of wire

$\begin{array}{ll} = ρ \cdot A (ρ = density) \\ = ρ (π r^{2}) or \sqrt{μ} \propto r \\ ∴ & v \propto \frac{1}{r l} \\ ∴ & \frac{v_{1}}{v_{2}} = (\frac{r_{2}}{r_{1}}) (\frac{l_{2}}{l_{1}}) = (\frac{r}{2 r}) (\frac{2 L}{L}) = 1 \end{array}$

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Wave Motion 2 Question 20

Answer:

इंजीनियरिंग की तैयारी

चिकित्सा तैयारी

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अन्य संसाधन

पाठ्यक्रम

परीक्षा मंच

नमूना मॉक टेस्ट

सदस्यता

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Wave Motion 2 Question 20

20. Two vibrating strings of the same material but of lengths L and 2L have radii 2r and r respectively. They are stretched under the same tension. Both the strings vibrate in their fundamental modes. The one of length L with frequency v1 and the other with frequency v2. The ratio v1/v2 is given by

Answer:

इंजीनियरिंग की तैयारी

चिकित्सा तैयारी

एनसीईआरटी पुस्तकें और समाधान

महत्वपूर्ण संसाधन

अन्य संसाधन

पाठ्यक्रम

परीक्षा मंच

नमूना मॉक टेस्ट

सदस्यता

एनसीईआरटी व्यायाम वीडियो समाधान

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