Q107 / 150 · MHT CET 2019 (Shift 2) · Physics

A stretched string fixed at both ends has ‘m’ nodes, then the length of the string will be

Correct answer
A
$(m - 1) \frac{λ}{2}$
B
$\frac{(m + 1) λ}{2}$
C
$\frac{m λ}{2}$
D
$(m - 2) \frac{λ}{2}$

Solution

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

l = \frac{p λ}{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 = \frac{(m - 1) λ}{2}

Hence, the correct answer is option: 'A'.

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