Question 5: Waves

Question

A pipe of length 85 cm is closed from one
end. Find the number of possible natural
oscillations of air column in the pipe whose
frequencies lie below 1250 Hz. The velocity
of sound in air is 340 m/s.

Accepted Answer

For closed organ pipe,
$$f=\frac{(2 n+1) v}{4 l} 	ext { (where, } n=0,1,2, ...)$$
According to question,
$$\begin{aligned}
\frac{(2 n+1) v}{4 l} & <1250 \\
2 n+1 & <\frac{1250 	imes 4 l}{v} \\
2 n+1 & <\frac{1250 	imes 4 	imes 0.85}{340} \\
\Rightarrow \quad 2 n & <11.5 \\
n & < 5.75
\end{aligned}$$
So $$n=0,1,2,3, \ldots 5$$.
So, we have 6 possibilities.

Answer

12

Answer

8

Answer

6

Answer

4

Waves

A pipe of length 85 cm is closed from one end. Find the number of possible natural oscillations of air column in the pipe whose frequencies lie below 1250 Hz. The velocity of sound in air is 340 m/s.

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