A string of length $1\text{ m}$ has the mass per unit length $0.1\text{g cm}^{-1}$. What would be the…
A string of length $1\text{ m}$ has the mass per unit length $0.1\text{g cm}^{-1}$. What would be the fundamental frequency of vibration of this string under tension of $400\text{ N}$?
$400\text{ Hz}$
$100\text{ Hz}$
$50\text{ Hz}$
$200\text{ Hz}$
Solution
Mass per unit length,
$\alpha = 0.1\text{ g cm}^{-1} = \frac{0.1 \times 10^{-3}}{10^{-2}} = 0.01\text{ kg m}^{-1}$
Velocity, $v = \sqrt{\frac{T}{\alpha}} = \sqrt{\frac{400}{0.01}} = 200\text{ ms}^{-1}$
Fundamental frequency of this string $= \frac{v}{2l} = \frac{200}{2 \times 1} = 100\text{ Hz}$