Question

A stretched string fixed at both ends has 'rrl nodes, then the length of the string will be ______.

Options

• `("m" - 1)lambda/2`

• `(("m" + 1)lambda)/2`

• `("m"lambda)/2`

• `("m - 2")lambda/2`

Answer 1

A stretched string fixed at both ends has 'rrl nodes, then the length of the string will be `underline(("m" - 1)lambda/2)`.

Explanation:

For p number of loops in a stretched string, the length is given by

l = `("p" lambda)/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`