A string of length 1m and mass 2 × 10 ^ - 5 kg is under tension T ....

Given: $l = 1m, m = 2 \times {10}^{– 5}kg$.

As successive harmonics are being given, so it is the case of both ends fixed.

Now,

${f}_{n + 1} - {f}_{n} = 1000 - 750$

$⇒ \dfrac{\left(n + 1\right)}{2l}\sqrt{\dfrac{T}{\mu}} - \dfrac{n}{2l}\sqrt{\dfrac{T}{\mu}} = 250$

$⇒ \dfrac{1}{2l}\sqrt{\dfrac{T}{\mu}} = 250$

$⇒ \sqrt{\dfrac{T}{2 \times {10}^{- 5}}} = 250 \times 2 \times 1$

$⇒ \dfrac{T}{2 \times {10}^{- 5}} = 25 \times {10}^{4}$

$⇒ T = 50 \times {10}^{- 1}$

$⇒ T = 5N$