First slide

Standing waves

Question

A stretched string of length 1m and mass 5 × $10^{- 4}$ kg, fixed at both ends, is under a tension of 20 N. If it is plucked at points situated at 25 cm from one end, it would vibrate with a frequency :

Moderate

A

400 Hz
B

200 Hz
C

100 Hz
D

256 Hz

Solution

Standing waves of produced in the string attached on both the ends, whose frequency is given by $\frac{n}{2 l} \sqrt{\frac{T}{μ}}$
$\begin{array}{l} T = 20 N \\ and μ = 5 \times 10^{- 4} \\ ∴ frequency = \frac{n}{2} \sqrt{4 \times 10^{4}} = 100 n \end{array}$
Now according to question the string is plucked at 25 cm
Thus antinode is present at 25 cm, thus $\frac{λ}{4} = 25 cm$
$λ = 100 cm$
$∴ n = 2$ , hence frequency = 200Hz

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