Question

A stretched string of one meter length, fixed at both the ends having mass of $5\times {10}^{-4}$ kg is under tension of 20 N. It is plucked at a point situated 25 cm from one end. The stretched string would vibrate with the frequency of:

• A. $400Hz$
• B. $100Hz$
• C. $256Hz$
• D. $200Hz$

Answer 1

Answer: (D)

$200Hz$

As we know plucking distance from one end $=\frac{l}{2p}$

$\Rightarrow 25=\frac{100}{2p}\Rightarrow p=2.$

Hence frequency of vibration

$n=\frac{p}{2l}\sqrt{\frac{T}{m}}=\frac{2}{2\times 1}\sqrt{\frac{20}{5\times {10}^{-4}}}=200Hz$