A sonometer wire of length 114 ~cm is fixed at both the ends. Where...

A sonometer wire of length

114 \mathrm{~cm}

is fixed at both the ends. Where should the two bridges be placed so as to divide the wire into three segments whose fundamental frequencies are in the ratio

1: 3: 4

Options

AAt $36 \mathrm{~cm}$ and $84 \mathrm{~cm}$ from one end
BAt $24 \mathrm{~cm}$ and $72 \mathrm{~cm}$ from one end
CAt $48 \mathrm{~cm}$ and $96 \mathrm{~cm}$ from one end
DAt $72 \mathrm{~cm}$ and $96 \mathrm{~cm}$ from one end

Correct answer

D. At $72 \mathrm{~cm}$ and $96 \mathrm{~cm}$ from one end

Step-by-step solution

Total length of the wire,

\mathrm{L}=114 \mathrm{~cm}\mathrm{n}_1: \mathrm{n}_2: \mathrm{n}_3=1: 3: 4

Let

\mathrm{L}_1, \mathrm{~L}_2

and

\mathrm{L}_3

be the lengths of the three parts As

\mathrm{n} \propto \frac{1}{\mathrm{~L}}

\begin{aligned}& \therefore \quad \mathrm{L}_{1}: \mathrm{L}_{2}: \mathrm{L}_{3}=\frac{1}{1}: \frac{1}{3}: \frac{1}{4}=12: 4: 3 \\ & \therefore \quad \mathrm{L}_{1}=72 \mathrm{~cm}\left(\frac{12}{12+4+3} \times114\right) \\ & \mathrm{L}_{2}=24 \mathrm{~cm}\left(\frac{4}{19} \times114\right) \\ & \text{\text{ and } } \quad \mathrm{L}_{3}=18 \mathrm{~cm}\left(\frac{3}{19} \times114\right) \end{aligned}

Hence

the bridges should be placed at72 \mathrm{~cm} and 72+24=96 \mathrm{~cm} from one end.

Practice Waves and Sound on Quantrex Academy →

More from Waves and Sound

List-I shows four configurations made of straight and semi-circular narrow tubes… JEE Advanced 2026 A transverse wave on a string is described by y = 3 (36t + 0.018x + π/4) , where x, y are… JEE Main 2026 The equation of a plane progressive wave is given by y = 5 π(200t - (x)/(150)) where x… JEE Main 2026 The speed of a longitudinal wave in a metallic bar is 400 ~m / s . If the density and… JEE Main 2026 Two tuning forks A and B are sounded together giving rise to 8 beats in 2 s. When fork A… JEE Main 2026 A point source is kept at the center of a spherically enclosed detector. If the volume of… JEE Main 2026 The fifth harmonic of a closed organ pipe is found to be in unison with the first… JEE Main 2026 The velocity of sound in air is doubled when the temperature is raised from 0^ ∘ C to α^… JEE Main 2026 Full Waves and Sound list All JEE Main PYQs