MHT-CET : Physics Entrance Exam

### MHT - CET : Physics - Stationary Waves Page 5

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7.

Melde's Experiment

Melde's experiment is useful to demonstrate the formation of transverse stationary waves and to determine the unknown frequency of a tuning fork.
The frequency of the tuning fork is determined by the formula

n =

 p 2l

 where, m: mass per unit length of the given light string T: Tension applied = mg where m: mass of the weights attached p: number of loops formed in the vibrating length 'l' of the string

Parallel or Longitudinal Position: In this position, the vibrations of the tuning fork are parallel to the length of the string.

Melde's Experiment (Parallel Position)
The string is attached to the prong of the tuning fork whose frequency is to be determined while the other end of the string passing over a pulley has a light pan attached at its free end. Tension is applied to the string by adding weights to the pan.

• In the parallel position, the frequency of the tuning fork is given by
N = 2
n
In parallel position of Melde's experiment, the vibrations proceed as follows:

(a)

Fork in rest position, string is straight.

(b)

Fork vibrates ® prongs bend
outwards
® string sags down

(c)

Prongs bend inwards ® string straightens.

(d)

Prongs again bend outwards ® string slacks upwards.

• Position (b) to (d)
® one vibration of fork
® half vibration of string.
Þ frequency of string is half the frequency of tuning fork.

n =

 N 2

\ N = 2n.

where

n =

 p 2l

= frequency of the vibrating string.

 \ N = p/l
• For a given frequency, P2T = constant (keeping l and m constant)

Melde's experiment (Perpendicular Position)

• In the perpendicular position, the frequency of the tuning fork (N) is given by

N = n =

 p 2l

where n =

 p 2l

= frequency of the vibrating string.

• In a given frequency, P2T = constant (keeping l and m constant).

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