Question

A string fixed at both ends has consecutive standing wave modes for which the distances between adjacent nodes are $18cm$ and $16cm$ respectively. The minimum possible length of the string is:

• A. $72cm$
• B. $144cm$
• C. $108cm$
• D. $216cm$

Answer 1

Answer: (B)

$144cm$

Let $n_1$ & $n_2$ be no.of loops when $18cm$ and $16cm$ are distances between nodes respectively.

$n_2-n_1=1$

Let $L$ be length of the string.

$L=18\times n_1$ & $L=16\times n_2$

Solving the three equations we get

$L=144cm$