A weight is attached to the free end of a sonometer wire It gives resonance at a length 40 - Physics - Motion In A Straight Line

Question

A weight is attached to the free end of a sonometer wire It gives
resonance at a length 40 cm when it is resonanced with a tuning
fork
of frequency 51 Hz The weight is then immersed wholly in water, the
resonant length is reduced to 30 cm The relative density in which
weight suspended is
(A) 16/9 (B) 16/7 (C) 16/5 (D) 16/3 Please also tell chapter name@
no links

Bakul Biswas · Accepted Answer

Dear Student,
frequencyf∝λwavelengthfor constant frequency,λ is proportinal to ω12λ1λ2=ω1ω212
(1)ω1=Df1 and ω2=Df1-Dwf1where,D is the density of material,Dw is the density of water
given,λ1=40 cm ,λ2=30 cm,f1=51 Hz,putting these values in equation(1)4030=Df1Df1-Dwf112=DD-Dw12DD-Dw12=43DD-Dw=169D-DwD=9161-DwD=916DwD=1-916=716DDw=167option(B) is correct

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