A sonometer wire resonates with a given tuning fork forming standing wave with 5 antinodes between two bridges when mass of 9 kg is suspended from the wire. When mass M is suspended from the wire with

Question

A sonometer wire resonates with a given tuning fork forming standing wave with 5 antinodes between two bridges when mass of 9 kg is suspended from the wire. When mass M is suspended from the wire with same fork and same length between two bridges, 3 antinodes are formed. Mass M is

TestHub · Accepted Answer

The frequency of a sonometer wire vibrating in $p$ loops (antinodes) is given by:

$f = \frac{p}{2 L} \frac{T}{μ}$

Since the tuning fork, length of the wire between the bridges, and mass per unit length are the same, $f$ , $L$ , and $μ$ are constant.

Therefore, $p T = constant$

$p_{1} T_{1} = p_{2} T_{2}$

Given $p_{1} = 5$ , $T_{1} = 9 g$ , $p_{2} = 3$ , and $T_{2} = M g$ :

$5 9 g = 3 M g$

$5 \times 3 = 3 M$

$M = 5$

$M = 25$ kg

Answer: $25$ kg

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