First slide

Standing waves

Question

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.

Moderate

A

4 gm
B

8 gm
C

2 gm
D

16 gm

Solution

In longitudinal mode: $\frac{n}{2} = \frac{p}{2 ℓ} \sqrt{\frac{T}{m}} or \frac{n}{2} = \frac{4}{2 ℓ} \sqrt{\frac{8}{m}} \dots . (1)$
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 : $n= \frac{q}{2 ℓ} \sqrt{\frac{T}{m}} or n = \frac{8}{2 ℓ} \sqrt{\frac{T}{m}} . . . . (2)$
dividing (1) by (2) we have $\frac{1}{2} = \frac{1}{2} \sqrt{\frac{8}{T}}$
T = 8 gm

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