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Q.

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 :

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a

400 Hz

b

200 Hz

c

100 Hz

d

256 Hz

answer is B.

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Detailed Solution

Standing waves of produced in the string attached on both the ends, whose frequency is given by  n2lTμT=20Nand   μ=5×10−4∴frequency=n24×104=100  nNow according to question the string is plucked at 25 cmThus antinode is present at 25 cm, thus λ4=25 cm  λ=100 cm ∴n=2, hence frequency = 200Hz
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