Question 281: Waves

Question

In an organ pipe closed at one end; the sum of the frequencies of first three overtones is 3930 Hz . The frequency of the fundamental mode of organ pipe is

Accepted Answer

Step 1: Understanding the overtones in a pipe closed at one end
In an organ pipe closed at one end, only odd harmonics are present.
Fundamental frequency (first harmonic): $f$
First overtone (third harmonic): $3f$
Second overtone (fifth harmonic): $5f$
Third overtone (seventh harmonic): $7f$
But the question asks for the first
three overtones
, i.e.,
First overtone = $3f$
Second overtone = $5f$
Third overtone = $7f$
Step 2: Writing the sum of first three overtones
Sum of frequencies:
$$ 3f + 5f + 7f = 15f $$
Given that:
$$ 15f = 3930 \, 	ext{Hz} $$
Step 3: Solving for fundamental frequency $f$
$$ f = \frac{3930}{15} $$
$$ f = 262\, 	ext{Hz} $$
Step 4: Final answer
The frequency of the fundamental mode of the organ pipe is
262 Hz
.
Correct option:
Option B (262 Hz)

Answer

256 Hz

Answer

262 Hz

Answer

320 Hz

Answer

384 Hz

Waves

In an organ pipe closed at one end; the sum of the frequencies of first three overtones is 3930 Hz . The frequency of the fundamental mode of organ pipe is

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