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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

A vibrating organ pipe has a fundamental frequency equal to 200 Hz .

A vibrating organ pipe has a fundamental frequency equal to 200 Hz200 \text{ Hz}.

Options

  1. AThe first overtone is exactly 400 Hz400 \text{ Hz}.
  2. BThe first overtone could be 400 Hz400 \text{ Hz}.
  3. CA frequency of 600 Hz600 \text{ Hz} is an overtone.
  4. DThe first overtone could be 600 Hz600 \text{ Hz}.

Correct answer

D. The first overtone could be 600 Hz600 \text{ Hz}.

Step-by-step solution

The organ pipe can be open at both ends or closed at one end.

For an open organ pipe, the frequencies of harmonics are given by f=nf0f = n f_0, where n=1,2,3,…n = 1, 2, 3, \dots
The fundamental frequency is f0=200 Hzf_0 = 200 \text{ Hz}.
The frequencies are 200 Hz,400 Hz,600 Hz,…200 \text{ Hz}, 400 \text{ Hz}, 600 \text{ Hz}, \dots
The first overtone is 400 Hz400 \text{ Hz} and the second overtone is 600 Hz600 \text{ Hz}.

For a closed organ pipe, the frequencies of harmonics are given by f=(2n−1)f0f = (2n-1) f_0, where n=1,2,3,…n = 1, 2, 3, \dots
The frequencies are 200 Hz,600 Hz,1000 Hz,…200 \text{ Hz}, 600 \text{ Hz}, 1000 \text{ Hz}, \dots
The first overtone is 600 Hz600 \text{ Hz}.

Thus, the first overtone could be 400 Hz400 \text{ Hz} (if the pipe is open) or 600 Hz600 \text{ Hz} (if the pipe is closed).
In both cases, 600 Hz600 \text{ Hz} is an overtone (second overtone for open pipe, first overtone for closed pipe).
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