MHT CET · Physics · Waves and Sound

When an open pipe is closed from one end then the third overtone of the closed pipe is higher in frequency by $150 Hz$ than the second overtone of an open pipe. The fundamental frequency of the open-end pipe will be

A $75 Hz$
B $150 Hz$
C $225 Hz$
D $300 Hz$

Verified Solution

Answer & Solution

Correct Answer

(D) $300 Hz$

Step-by-step Solution

Detailed explanation

Let

f_{0} = \frac{v_{0}}{2 L}

be the fundamental frequency of the open pipe

∴

is second overtone is

3 f_{0} = \frac{3 v_{0}}{2 L}

Let

f = \frac{v_{0}}{4 L}

be the fundamental frequency of close pipe.
And third overtone of the organ pipe closed at one end only is,

{(f_{3})}_{c l o s e d} = \frac{7}{4} \frac{v_{0}}{L}

As given

\frac{7 v_{0}}{4 L} - \frac{3 v_{0}}{2 L} = 150

(\frac{7}{4} - \frac{6}{4}) \frac{v_{0}}{L} = 150

∴ \frac{v_{0}}{4 L} = 150

\frac{v_{0}}{2 L} = 300 Hz

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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When an open pipe is closed from one end then the third overtone of the closed pipe is higher in frequency by 150 Hz than the second overtone of an open pipe. The fundamental frequency of the open-end pipe will be

Step-by-step Solution

When an open pipe is closed from one end then the third overtone of the closed pipe is higher in frequency by $150 Hz$ than the second overtone of an open pipe. The fundamental frequency of the open-end pipe will be