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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

The fundamental frequency of an open organ pipe P_2 is identical to...

The fundamental frequency of an open organ pipe

P_2

is identical to the first overtone frequency of a closed organ pipe

P_1

. If pipe

P_1

has a length of

30 \text{ cm}

, what is the length of

P_2

?

Options

A $10 \text{ cm}$
B $45 \text{ cm}$
C $30 \text{ cm}$
D $20 \text{ cm}$

Correct answer

D. $20 \text{ cm}$

Step-by-step solution

For a closed organ pipe

P_1

of length

L_1

, the first overtone frequency is given by

f_1 = \dfrac{3v}{4L_1}

For an open organ pipe

P_2

of length

L_2

, the fundamental frequency is given by

f_2 = \dfrac{v}{2L_2}

Given that

f_1 = f_2

\dfrac{3v}{4L_1} = \dfrac{v}{2L_2}

L_2 = \dfrac{2L_1}{3}

Substituting

L_1 = 30 \text{ cm}

L_2 = \dfrac{2 \times 30}{3} = 20 \text{ cm}

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