Question

A wire is under tension of \(2\) kg wt and a wave is travelling through it with some speed. Tension in the wire is so increased that the wave travels through it with thrice the original speed. The increase in tension is (in kg wt)

• A. \(4\)
• B. \(8\)
• C. \(16\)
• D. \(12\)

Hint:

Wave speed is the square root of tension over mass per length.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
The speed of a transverse wave on a string is \(v=\sqrt{T/\mu}\), so \(v^2\propto T\) for the same wire.

Step 2: Apply:
If the speed becomes 3 times, the tension becomes \(3^2=9\) times. So
\[ T'=9\times2=18\ \text{kg wt} \]

Step 3: Increase:
\[ 18-2=16\ \text{kg wt} \]

Step 4: Choose:
Option (C). The value 12 would come from adding 6 instead of multiplying tension by 9.

Final Answer:
The tension must rise by 16 kg wt. \[ \boxed{16\ \text{kg wt}} \]