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ICSE Class 10 Physics 2017 Paper

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Question : 50 of 65
Marks: +1, -0
A wire of length 80 cm80\ \mathrm{cm} has a frequency of 256 Hz256\ \mathrm{Hz}. Calculate the length of a similar wire under similar tension, which will have frequency 1024 Hz1024\ \mathrm{Hz} .
Solution:  
Given : l1=80 cm,n1=256 Hz,l2=l_1=80\ \mathrm{cm}, n_1=256\ \mathrm{Hz}, l_2= ?, n2=1024 Hzn_2=1024\ \mathrm{Hz}
We know,     n∝  1l\;\; n \propto \;\frac{1}{l}
(If tension ' TT ' is constant)
  ∴    n1l1=n2l2\; \therefore \;\; n_1 l_1 = n_2 l_2
or   l2=n1l1n2=256×801024\; l_2 = \frac{n_1 l_1}{n_2} = \frac{256 \times 80}{1024}
  =20 cm  .   \; = 20\ \mathrm{cm} \; \text{. } \;
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