Standing Wave in String and Organ Pipe

Question 31: easy

Assertion (A): A tuning fork is in resonance with a closed pipe in fundamental mode, but the same tuning fork cannot be in resonance in fundamental mode with an open pipe of same length.

Reason (R): The same tuning fork will not be in resonance with open pipe of same length due to end correction of pipe.

1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)

2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)

3. (A) is true but (R) is false

4. Both (A) and (R) are false

View Answer

Assertion (A) is true. For a closed pipe of length \(L\), fundamental frequency is \(v/(4L)\). For an open pipe of same length, it's \(v/(2L)\). These are different, so the same tuning fork cannot resonate in fundamental mode with both. Reason (R) is false; the primary reason is the fundamental frequency difference (\(f_o = 2f_c\)), not solely end correction.

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