First slide

Standing waves

Question

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

Moderate

A

250,255
B

255,260
C

260,265
D

265,270

Solution

$n_{1} = \frac{V}{4 l_{1}} and n_{2} = \frac{V}{4 l_{2}} â´ \frac{n_{1}}{n_{2}} = \frac{l_{2}}{l_{1}} = \frac{50}{51} Given that, n_{2} = n_{1} + 5 \frac{n_{1}}{n_{1} + 5} = \frac{50}{51} or n_{1} = 250 Hz Now n_{2} = 250 + 5 = 255 Hz$

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