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 in order to raise the wave speed by 20% is
The speed of a wave on a string is 150 m/s when the tension is 120 N. The percentage increase in the tension in order to raise the wave speed by 20% is
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\(v \propto \sqrt{T}\). For 20% increase in speed, tension increases by 44%.
Updated On: Apr 23, 2026
- 44%
- 40%
- 20%
- 10%
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The Correct Option is A
Solution and Explanation
Step 1: Understanding the Concept:
Wave speed on string: \(v = \sqrt{\frac{T}{\mu}}\). So \(v \propto \sqrt{T}\).
Step 2: Detailed Explanation:
New speed \(v' = v + 20%v = 1.2v\).
\(\frac{v'}{v} = \sqrt{\frac{T'}{T}} \Rightarrow 1.2 = \sqrt{\frac{T'}{T}} \Rightarrow \frac{T'}{T} = (1.2)^2 = 1.44\).
Percentage increase = \((1.44 - 1) \times 100 = 44%\).
Step 3: Final Answer:
Thus, tension must increase by 44%.
Wave speed on string: \(v = \sqrt{\frac{T}{\mu}}\). So \(v \propto \sqrt{T}\).
Step 2: Detailed Explanation:
New speed \(v' = v + 20%v = 1.2v\).
\(\frac{v'}{v} = \sqrt{\frac{T'}{T}} \Rightarrow 1.2 = \sqrt{\frac{T'}{T}} \Rightarrow \frac{T'}{T} = (1.2)^2 = 1.44\).
Percentage increase = \((1.44 - 1) \times 100 = 44%\).
Step 3: Final Answer:
Thus, tension must increase by 44%.
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