MHT CET · Physics · Waves and Sound

The fundamental frequency of an air column in a pipe closed at one end is $100 Hz$ . If the same pipe is open at both the ends, the frequencies produced in $Hz$ are

A 100, 200, 300, 400, .....
B 100, 300, 500, 700, .....
C 200, 300, 400, 500 ,....
D 200, 400, 600, 800, .....

Verified Solution

Answer & Solution

Correct Answer

(D) 200, 400, 600, 800, .....

Step-by-step Solution

Detailed explanation

For a closed pipe fundamental frequency

n_{1} = \frac{V}{4 L} = 100 Hz

For an open pipe fundamental frequency

{n'}_{1} = \frac{V}{2 L} = 2 n_{1} = 200 Hz

In an open pipe all multiples of the fundamental are produced.

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.

Same subject

Explore more questions on app

From MHT CET

Explore more questions on app

The fundamental frequency of an air column in a pipe closed at one end is 100 Hz. If the same pipe is open at both the ends, the frequencies produced in Hz are

Step-by-step Solution

The fundamental frequency of an air column in a pipe closed at one end is $100 Hz$ . If the same pipe is open at both the ends, the frequencies produced in $Hz$ are