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: Understanding the Concept:
\(f = \frac{1}{2l}\sqrt{\frac Tm}\), so \(f\propto\sqrt T\) and \(T\propto f^2\).

Step 2: Calculation:
The frequency rises by 40 percent, so \(f' = 1.4f\). Then \(T' = (1.4)^2T = 1.96T\).

Step 3: Percentage:
The tension increases by \(1.96 - 1 = 0.96\), that is 96 percent. Choosing 40 percent would ignore the square, and 100 percent would be a doubling.

Final Answer:
Tension must be increased by 96 percent, option (C). \[ \boxed{96\%} \]