Question

The speed of a wave on a string is \(150\) m/s when the tension is \(120\) N. The percentage increase in the tension to raise the wave speed by \(20\%\) is

• A. \(44\%\)
• B. \(40\%\)
• C. \(20\%\)
• D. \(10\%\)

Hint:

Wave speed on a string is proportional to the square root of tension. A 20 percent speed rise means the tension is multiplied by 1.2 squared.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept
\(v=\sqrt{\frac{T}{\mu}}\), so \(T\propto v^{2}\) for a fixed string.

Step 2: New Speed
A 20% increase gives \(v'=1.2v\).

Step 3: Tension Ratio
\(\dfrac{T'}{T}=\left(\dfrac{v'}{v}\right)^{2}=1.2^{2}=1.44\).

Step 4: Percentage Increase
\((1.44-1)\times100=44\%\).

Final Answer:
The tension must increase by 44 percent. \[ \boxed{\text{(A) }44\%} \]