Question

If there are six loops for 1 m length in transverse mode of Melde's experiment., the no. of loops in longitudinal mode under otherwise identical condition would be
A. 3
B. 6
C. 12
D. 8

Answer 1

Hint: The longitudinal mode is generally the tuning fork which is used to make the tensed string vibrate in transverse mode. One loop of the string contains two nodes and one antinode.

Complete step by step solution:
When the tension is applied on the string and a disturbance is induced at one end, the disturbance travels through the length of the string and if the other end is rigid then it encounters reflection from the rigid end. The incoming reflected wave moves in the opposite direction from the stationary point which is called a node. These waves are called the standing wave.

The standing wave is the combination of the maximum vertical displacement in either direction of the mean position. When the tuning fork vibrates once, then there are two consecutive maximum vertical displacements in upward and downward direction. Hence, one loop of the longitudinal mode in turning form produces two loops in the string.

So, the number of loops in the longitudinal mode is half the number of loops in the transverse mode. It is given that there are six loops for 1 meter length in the transverse mode of Melde’s experiments. So, number of loops in the longitudinal mode is,
\[\dfrac{6}{2} = 3\]
Hence, if there are 6 loops in the transverse mode, then there are 3 loops in the longitudinal mode.

Therefore, the correct option is A.

Note: In normal transverse waves one maximum displacement in upward and one maximum displacement in downward completes one cycle. In a standing wave, one cycle is two nodes and one antinode.