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Waves question

2016 · Q159
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Waves question

2016 · Q159

NEETPhysicsWavesMCQ+4 / −1
A uniform rope of length L and mass m1 hangs vertically from a rigid support. A block of mass m2 is attached to the free end of the rope. A transverse pulse of wavelength λ\lambdaλ1 is produced at the lower end of the rope. The wavelength of the pulse when it reaches the top of the rope is λ\lambdaλ2. The ratio λ\lambdaλ2/λ\lambdaλ1 is
  1. A
    m2m1\sqrt {{{{m_2}} \over {{m_1}}}}m1​m2​​​
  2. B
    m1+m2m1\sqrt {{{{m_1} + {m_2}} \over {{m_1}}}}m1​m1​+m2​​​
  3. C
    m1m2\sqrt {{{{m_1}} \over {{m_2}}}}m2​m1​​​
  4. D
    m1+m2m2\sqrt {{{{m_1} + {m_2}} \over {{m_2}}}}m2​m1​+m2​​​
View written solutionFree

Correct answer: D

NEET 2016 Phase 1 Physics - Waves Question 54 English Explanation

Wavelength of pulse at the lower end

λ1∝velocity(v1)=T1μ{\lambda _1} \propto velocity({v_1}) = \sqrt {{{{T_1}} \over \mu }} λ1​∝velocity(v1​)=μT1​​​

Similarly, λ1∝v2{\lambda _1} \propto {v_2}λ1​∝v2​ =T2μ= \sqrt {{{{T_2}} \over \mu }}=μT2​​​

∴\therefore∴ λ2λ1=T2T1=(m1+m2)gm2g{{{\lambda _2}} \over {{\lambda _1}}} = \sqrt {{{{T_2}} \over {{T_1}}}} = \sqrt {{{\left( {{m_1} + {m_2}} \right)g} \over {{m_2}g}}} λ1​λ2​​=T1​T2​​​=m2​g(m1​+m2​)g​​

=m1+m2m2= \sqrt {{{{m_1} + {m_2}} \over {{m_2}}}}=m2​m1​+m2​​​

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