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Concepts Of Physics MCQ Edition [Volume 1]

Exam: Concepts Of Physics MCQ Edition [Volume 1]
Subject: Physics
Chapter: Sound Waves

Concepts Of Physics MCQ Edition [Volume 1] · Physics · Sound Waves

Determine the fundamental, first overtone, and second overtone...

Determine the fundamental, first overtone, and second overtone frequencies of an open organ pipe having a length of

20 \text{ cm}

. The speed of sound in air is

340 \text{ m s}^{-1}

.

Options

A $850 \text{ Hz}$ , $2550 \text{ Hz}$ , and $4250 \text{ Hz}$
B $425 \text{ Hz}$ , $1275 \text{ Hz}$ , and $2125 \text{ Hz}$
C $1700 \text{ Hz}$ , $3400 \text{ Hz}$ , and $5100 \text{ Hz}$
D $850 \text{ Hz}$ , $1700 \text{ Hz}$ , and $2550 \text{ Hz}$

Correct answer

D. $850 \text{ Hz}$ , $1700 \text{ Hz}$ , and $2550 \text{ Hz}$

Step-by-step solution

For an open organ pipe, the fundamental frequency is given by

f_1 = \dfrac{v}{2L}

Substituting the given values,

v = 340 \text{ m s}^{-1}

and

L = 20 \text{ cm} = 0.2 \text{ m}

:

f_1 = \dfrac{340}{2 \times 0.2} = \dfrac{340}{0.4} = 850 \text{ Hz}

The first overtone corresponds to the second harmonic,

f_2 = 2f_1

:

f_2 = 2 \times 850 = 1700 \text{ Hz}

The second overtone corresponds to the third harmonic,

f_3 = 3f_1

:

f_3 = 3 \times 850 = 2550 \text{ Hz}

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