A stretched string fixed at both end has n nods, then the lengths of the string is

Options

A. `(m-1)(lambda)/(2)`
B. `((m+1)lambda)/(2)`
C. `(mlambda)/(2)`
D. `(m -2)(lambda)/(2)`

Answer

A

Explanation

For p number of loops in a stretched string, the length is given by
`l = (plambda)/(2)" "……..(i)`
As, number of harmonics = number of loops = number of anti - nodes = P `" "……….(ii)`
Also , number of nodes = number of anti - nodes + 1 .
Here, number of nodes = m
Number of anti - nodes = m - 1 from Eq.(ii)
`p = m - 1`
Putting this value of p in Eq.(i) we get
`l = ((m -1)lambda)/(2)`