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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
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
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Solution
The correct option is A 3
One cycle of up and down vibration for transverse waves on the string is two cycles of string tension increase and decrease. The tension is maximum both at the loops’ maximum up position and again at maximum down position. Therefore, in longitudinal drive mode, since the string tension increases and decreases once per tuning fork vibration, it takes one tuning fork vibration to move the string loop to maximum up position and one to move it to maximum down position. This is two tuning fork vibrations for one up and down string vibration, so the tuning fork frequency is half the string frequency.
Hence, the number of loops in longitudinal mode(tuning fork) is half of that of transverse mode(string).
One cycle of up and down vibration for transverse waves on the string is two cycles of string tension increase and decrease. The tension is maximum both at the loops’ maximum up position and again at maximum down position. Therefore, in longitudinal drive mode, since the string tension increases and decreases once per tuning fork vibration, it takes one tuning fork vibration to move the string loop to maximum up position and one to move it to maximum down position. This is two tuning fork vibrations for one up and down string vibration, so the tuning fork frequency is half the string frequency.
Hence, the number of loops in longitudinal mode(tuning fork) is half of that of transverse mode(string).
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