Question

In a pipe closed at one end, air column is vibrating in the fourth overtone so the vibrating air column has '\(x\)' nodes and '\(y\)' antinodes. The values of \(x\) and \(y\) are respectively

• A. \(4,4\)
• B. \(4,5\)
• C. \(5,4\)
• D. \(5,5\)

Hint:

Frequency of a stretched string goes as the square root of tension.

Answer 1

The Correct Option is D

Step 1: Ratio method:
$\frac{T'}{T} = \left(\frac{f'}{f}\right)^2 = \left(\frac{140}{100}\right)^2 = \frac{196}{100}$.

Step 2: Increase:
$\frac{196 - 100}{100}\times100 = 96$ percent (C).

Final Answer:
96 percent. \[ \boxed{96\%} \]