Question

A sonometer wire of length 114 cm is fixed at the 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?

• A. at 36 cm and 84 cm from one end
• B. at 24 cmand 72 cm from one end
• C. at 48 cm and 96 cm from one end
• D. at 72 cm and 96 cm from one end

Answer 1

The correct option is D at 72 cm and 96 cm from one end

Given: Length of the sonometer wire = 114 cm

Solution: Let the bridges divides the whole length in three parts as $l_1,l_2,l_3$

According to question,

$n_1:n_2:n_3=1:3:4$

Also,

$n\propto \frac{1}{l}$

So, $l_1:l_2:l_3=\frac{1}{1}:\frac{1}{3}:\frac{1}{4}$

$l_1:l_2:l_3=12:4:3$

O solving,

$l_1$=72 cm

$l_2=18cm$

Therefore, the two bridges must be placed at 72 cm from one end and (72+18=96) 96 cm from the other end.

Hence, the correct option is (D).