A tube closed at one end has a length of 0.85\text{ m}. If the speed of sound in air is 34… — JAMB UTME

A tube closed at one end has a length of $0.85\text{ m}$ . If the speed of sound in air is $340\text{ m/s}$ , what is the fundamental frequency of the sound wave produced in the tube?

$100\text{ Hz}$ Answer
B
$200\text{ Hz}$
C
$400\text{ Hz}$
D
$289\text{ Hz}$

Answer

100\text{ Hz}

For a pipe closed at one end, the fundamental frequency is given by

f = \frac{v}{4L}

. Substituting

v = 340\text{ m/s}

and

L = 0.85\text{ m}

yields

f = \frac{340}{4 \times 0.85} = \frac{340}{3.4} = 100\text{ Hz}

Step-by-Step Solution

Determine the relationship between pipe length and wavelength for the fundamental mode of a closed pipe.

For a pipe closed at one end,

\lambda = 4L = 4 \times 0.85\text{ m} = 3.4\text{ m}

A closed tube forms a node at the closed end and an antinode at the open end, corresponding to one quarter of a full wavelength.

Calculate fundamental frequency using the wave equation

v = f\lambda

f = \frac{v}{\lambda} = \frac{340\text{ m/s}}{3.4\text{ m}} = 100\text{ Hz}

Frequency equals wave velocity divided by fundamental wavelength.

Key Concept

Fundamental frequency of a pipe closed at one end

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