Waves · Question 57

A string is cut into three parts, having fundamental frequencies n1, n2, n3 respectively. Then original fundamental frequency n related by the expression as

1. 1n = 1n1 + 1n2 + 1n3
2. n = n1 n2 n3
3. n = n1 + n2 + n3
4. n = n1 + n2 + n33

Answer

(1) 1n = 1n1 + 1n2 + 1n3

Solution

Fundamental frequency of a stretched string: n = 12l T

For the same tension T and mass per unit length : n 1l, i.e. l = kn

Since the string is cut into three parts, l = l1 + l2 + l3

kn = kn1 + kn2 + kn3

1n = 1n1 + 1n2 + 1n3

Answer: (1)