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Waves question

2014 · Q158
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Waves question

2014 · Q158

NEETPhysicsWavesMCQ+4 / −1
If n1, n2 and n3 are the fundamental frequencies of three segments into which a string is divided, then the original fundamental frequency n of the string is given by
  1. A
    1n=1n1+1n2+1n3{1 \over n} = {1 \over {{n_1}}} + {1 \over {{n_2}}} + {1 \over {{n_3}}}n1​=n1​1​+n2​1​+n3​1​
  2. B
    1n=1n1+1n2+1n3{1 \over {\sqrt n }} = {1 \over {\sqrt {{n_1}} }} + {1 \over {\sqrt {{n_2}} }} + {1 \over {\sqrt {{n_3}} }}n​1​=n1​​1​+n2​​1​+n3​​1​
  3. C
    n=n1+n2+n3\sqrt n = \sqrt {{n_1}} + \sqrt {{n_2}} + \sqrt {{n_3}}n​=n1​​+n2​​+n3​​
  4. D
    n === n1 + n2 + n3
View written solutionFree

Correct answer: A

AIPMT 2014 Physics - Waves Question 49 English Explanation

n=12lTmn = {1 \over {2l}}\sqrt {{T \over m}} n=2l1​mT​​

⇒n∝1l⇒nl=constant, K \Rightarrow n \propto {1 \over l} \Rightarrow nl = constant,\,K⇒n∝l1​⇒nl=constant,K

∴\therefore∴ n1l1=K,n2l2=K,n3l3=K{n_1}{l_1} = K,{n_2}{l_2} = K,{n_3}{l_3} = Kn1​l1​=K,n2​l2​=K,n3​l3​=K

Also, l=l1+l2+l3l = {l_1} + {l_2} + {l_3}l=l1​+l2​+l3​

⇒Kn=Kn1+Kn2+Kn3 \Rightarrow {K \over n} = {K \over {{n_1}}} + {K \over {{n_2}}} + {K \over {{n_3}}}⇒nK​=n1​K​+n2​K​+n3​K​

⇒1n=1n1+1n2+1n3 \Rightarrow {1 \over n} = {1 \over {{n_1}}} + {1 \over {{n_2}}} + {1 \over {{n_3}}}⇒n1​=n1​1​+n2​1​+n3​1​

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