A fundamental harmonic standing wave is generated in a string fixed at both ends. If the tension in the string is increased by \(21\%\), the percentage change in the fundamental frequency will be:
Show Hint
For large percentage increases (like \(21\%\)), do not use the small-error differential approximation (\(\Delta f / f \approx \frac{1}{2} \Delta T / T\)), as that shortcut is strictly meant for variations under \(5\%\). Instead, seek out perfect squares hidden in the decimals (like \(1.21 = 1.1^2\) or \(1.44 = 1.2^2\)) to quickly pull values out of the radical!