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Q.

Two organ pipes, each closed at one end, give 5 beats per second when emitting their fundamental notes. If their lengths are in the ratio of 50 : 51, their fundamental frequencies (in Hz) are

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a

250,255

b

255,260

c

260,265

d

265,270

answer is A.

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Detailed Solution

v1 =14L1 γPρ,v2 =14L2 γPρ.Thereforev1 v2 =L2 L1 =5051. It is given that v2 =v1 +5Therefore v1 v1 +5=5051which gives v1 =250Hz.Hence v2 =250+5=255Hz which is choice (a)

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Two organ pipes, each closed at one end, give 5 beats per second when emitting their fundamental notes. If their lengths are in the ratio of 50 : 51, their fundamental frequencies (in Hz) are