The number of possible natural oscillations of air column in a pipe closed at one end of length $$85$$ cm whose frequencies lie below $$1250$$ Hz are (Velocity$$ of sound $$=$$ $$340$$ m $$s-1)

Question

The number of possible natural oscillations of air column in a pipe closed at one end of length $$85$$ cm whose frequencies lie below $$1250$$ Hz are (Velocity$$ of sound $$=$$ $$340$$ m $$s-1)

Infinity Learn · Accepted Answer

Fundamental frequency of the closed organ pipe $$isv=v4L$$ Here, $$v=340$$ m $$s-1$$,$$L=85$$ $$cm=0.85$$ m∴  $$v=340$$ m $$s-14$$×$$0.85$$ $$m=100$$ HzThe natural frequencies of the closed organ pipe will $$bevn=(2n-1)v=v$$,$$3v$$,$$5v$$,$$7v$$,$$9v$$,$$11v$$,$$13v$$,…       $$=100$$ Hz,$$300$$ Hz,$$500$$ Hz,$$700$$ Hz,$$900$$ Hz                                                 $$1100$$ Hz,$$1300$$ Hz,… and so on. Thus, the natural frequencies lies below the $$1250$$ Hz is $$6$$.

The number of possible natural oscillations of air column in a pipe closed at one end of length 85 cm whose frequencies lie below 1250 Hz are (Velocity of sound = 340 m $s^{- 1}$ )

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The number of possible natural oscillations of air column in a pipe closed at one end of length 85 cm whose frequencies lie below 1250 Hz are (Velocity of sound = 340 m s-1)

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The number of possible natural oscillations of air column in a pipe closed at one end of length 85 cm whose frequencies lie below 1250 Hz are (Velocity of sound = 340 m $s^{- 1}$ )