If the velocity of sound in air is 320 m / s, then (maximum and minimum audible frequency are 2

step 1 In this question we have given the velocity of sound in air that is 320 meter per second and max

If the velocity of sound in air is 320 m / s, then (maximum...

If the velocity of sound in air is $320 \mathrm{~m} / \mathrm{s}$, then (maximum and minimum audible frequency are $20 \mathrm{~Hz}$ and $20000 \mathrm{~Hz}$, respectively), the maximum and minimum lengths of a closed pipe that would produce a just audible sound are (A) $2.6 \mathrm{~m}$ and $3.6 \times 10^{-3} \mathrm{~m}$ (B) $4 \mathrm{~m}$ and $4.2 \times 10^{-3} \mathrm{~m}$ (C) $3 \mathrm{~m}$ and $3 \times 10^{-3} \mathrm{~m}$ (D) $4 \mathrm{~m}$ and $4 \times 10^{-3} \mathrm{~m}$

If the velocity of sound in air is $320 \mathrm{~m} / \mathrm{s}$, then (maximum and minimum audible frequency are $20 \mathrm{~Hz}$ and $20000 \mathrm{~Hz}$, respectively), the maximum and minimum lengths of a closed pipe that would produce a just audible sound are
(A) $2.6 \mathrm{~m}$ and $3.6 \times 10^{-3} \mathrm{~m}$
(B) $4 \mathrm{~m}$ and $4.2 \times 10^{-3} \mathrm{~m}$
(C) $3 \mathrm{~m}$ and $3 \times 10^{-3} \mathrm{~m}$
(D) $4 \mathrm{~m}$ and $4 \times 10^{-3} \mathrm{~m}$

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Key Concepts

Resonance in Closed Pipes

Resonance occurs in a closed pipe when the length of the pipe supports a standing wave pattern that satisfies the boundary conditions, specifically having a node at the closed end and an antinode at the open end. This leads to the fundamental mode of vibration and its harmonic series, which determine the resonant frequencies of the pipe.

Fundamental Frequency in a Closed Pipe

For a pipe closed at one end, the fundamental frequency corresponds to a standing wave with a wavelength that is four times the length of the pipe (? = 4L). This relationship, expressed as f = v / (4L), is used to calculate the minimal or maximal physical dimensions of a pipe required to produce a particular audible frequency.

Speed of Sound

This is the rate at which sound waves travel through a medium such as air. It is crucial in determining the wavelength of a sound wave for a given frequency using the relationship v = f×?. The value of the speed of sound directly influences the calculations of resonance conditions in acoustic systems.

Frequency and Wavelength Relationship

This key concept states that the speed of a wave is the product of its frequency and wavelength (v = f×?). In acoustics, this relationship is fundamental in linking audible frequencies with the physical dimensions of the sound producing apparatus.

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