In Melde’s experiments in the longitudinal mode of vibration a string vibrates in 4 loops with a load of 8 gm. How much load would be required in order that the string many vibrate in 8 loops in transverse mode.

In longitudinal mode:$\frac{\mathrm{n}}{2}=\frac{\mathrm{p}}{2\mathrm{\ell }}\sqrt{\frac{\mathrm{T}}{\mathrm{m}}} \mathrm{or} \frac{\mathrm{n}}{2}=\frac{4}{2\mathrm{\ell }}\sqrt{\frac{8}{\mathrm{m}}}\dots .\left(1\right)$
Note: Transverse position in Melde's experiment is changed to parallel position. If length of the string remains the same and tension is made half and if in perpendicular position 4 loops are formed then the number of logps formed in parallel position will be 2{ no of loops}.
In transrverse mode :$\text{n=}\frac{\mathrm{q}}{2\mathrm{\ell }}\sqrt{\frac{\mathrm{T}}{\mathrm{m}}} \mathrm{or} \mathrm{n}=\frac{8}{2\mathrm{\ell }}\sqrt{\frac{\mathrm{T}}{\mathrm{m}}} . . . . \left(2\right)$
dividing (1) by (2) we have $\frac{1}{2}=\frac{1}{2}\sqrt{\frac{8}{\mathrm{T}}}$
T = 8 gm