Question

A stretched wire of length 114cm is divided into three segments whose frequencies are in the ratio 1 : 3 : 4, the lengths of the segments must be in the ratio​

Answer 1

Given:

Length of the wire = 114cm

Ratio of three segments = 1 : 3 : 4

To find:

The ratio of length segments

Solution:

f ∝ 1/l

Ratio of lengths = 1: 3: 4

= f1: f2 : f3 = 1 : 3: 4

= 1/l1 + 1/l2 + 1/l3 = 1 : 3: 4

Thus l1 : l2: l3 = 1: 1/3 : 1/4

Now,

1 + 1/3 + 1/4

= 19/12

Calculating the ratio with given ratios

114 ×  12 × (1/19)

= 72

114 ×  12 × (1/3)/19

= 24

114 ×  12 × (1/4)/19

= 18

Answer: The ratio of three segments is 72:24:18 or 12:4:3