Two vibrating strings of the same material but length L and $$2L$$ have radii $$2r$$ and r respectively . They are stretched under the same tension. Both strings vibrates in their fundamental nodes. The one of length ‘L’ with frequency $$n1$$ and other with frequency $$n2$$ . The ratio of $$n1/n2$$ is given

Question

Two vibrating strings of the same material but length L and $$2L$$ have radii $$2r$$ and r respectively . They are stretched under the same tension. Both strings vibrates in their fundamental nodes. The one of length ‘L’ with frequency  $$n1$$ and other with frequency $$n2$$ .  The ratio of  $$n1/n2$$ is given

Infinity Learn · Accepted Answer

Fundamental frequency for first string  : $$n1=12lT4$$$$π$$$$r2$$ρ                                                                   ⇒ $$n1=14lT$$$$π$$$$r2$$ρ  →  $$1$$   and  Fundamental frequency for second string  : $$n2=12(2l)T$$$$π$$$$r2$$ρ    → $$2$$  Divide $$i/ii$$                        $$n1n2=1$$

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Two vibrating strings of the same material but length L and 2L have radii 2r and r respectively . They are stretched under the same tension. Both strings vibrates in their fundamental nodes. The one of length ‘L’ with frequency n1 and other with frequency n2 . The ratio of n1/n2 is given

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