First slide

Stationary waves

Question

Two closed pipe produce 10 beats per second when emitting their fundamental nodes. If their length are in ratio of 25 : 26. Then their fundamental frequency in Hz, are

Moderate

A

270, 280
B

260, 270
C

260, 250
D

260, 280

Solution

$n_{1} - n_{2} = 10$ ..…(i)
Using $n_{1} = \frac{v}{4 l_{1}}$ and $n_{2} = \frac{v}{4 l_{2}}$
$\Rightarrow \frac{n_{1}}{n_{2}} = \frac{l_{2}}{l_{1}} = \frac{26}{25}$ …..(ii)
After solving these equation $n_{1} = 260 Hz, n_{2} = 250 Hz$

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