Question 167: 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

Length of pipe $$=85$$ $$cm$$ $$=0.85m$$
Pipe is closed from one end so it behaves as a closed organ pipe
Frequency of oscillations of air column in closed organ pipe is given by,
$$f = {{\left( {2n - 1} ight)\upsilon } \over {4L}}$$
$$f = {{\left( {2n - 1} ight)\upsilon } \over {4L}} \le 1250$$
$$ \Rightarrow {{\left( {2n - 1} ight) 	imes 340} \over {0.85 	imes 4}} \le 1250$$
$$ \Rightarrow 2n - 1 \le 12.5 \approx 6$$
Possible value of n = 1, 2, 3, 4, 5, 6
So, number of possible natural frequencies lie below 1250 Hz is 6.

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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