The pipe of length $$l1$$ , closed at one end is kept in a chamber of gas of density ρ$$1$$. A second pipe open at both ends is placed in a second chamber of gas density ρ$$2$$, the compressibility of both gases is equal. Calculate length of the second pipe if frequency of first one in both the cases are equal.

Question

The pipe of length $$l1$$ , closed at one end is kept in a chamber of gas of density ρ$$1$$. A second pipe open at both ends is placed in a second chamber of gas density ρ$$2$$, the compressibility of both gases is equal. Calculate length of the second pipe if frequency of first one in both the cases are equal.

Infinity Learn · Accepted Answer

Frequency of first overtone in closed pipe $$f=34l1P$$ρ$$1$$     → $$1$$  Frequency of first overtone in open pipe  f'$$=22l2P$$ρ$$2$$      →  $$2$$  equating (1) & (2)  $$l2=43l1$$ρ$$1$$ρ$$2$$

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