pHYSICS

Experiment 2

Aim of the Experiment

To determine the frequency of an electrically maintained tuning fork by,

1. Transverse mode of vibration

2. Longitudinal mode of vibration

Principle

Speed of waves in a stretched string: A string means a wire or a fiber which has a uniform diameter and is perfectly flexible. The speed of a wave in a flexible stretched string depends upon the tension in the string and mass per unit length of the string.

Where the tension T in the string equal to Mg.

M - Mass suspended and g is acceleration due to gravity.

μ - linear density or mass per unit length of the string.

Where m is the mass of the string and L is the total length of the string.

Vibrations of a stretched string: When the wire is clamped to a rigid support, the transverse progressive waves travel towards each end of the wire. By the superposition of incident and reflected waves, transverse stationary waves are set up in the wire. Since ends of the wire are clamped, there is node N at each end and anti node A in the middle as shown in Fig: 1.

The points of the medium which have no displacements called nodes and there are some points which vibrate with maximum amplitude called antinodes.

The distance between two consecutive nodes is λ/2, ( λ - wavelength). Because l is half a wavelength in the equations,

If ‘f’ be the frequency of vibration the wire,

Substituting the value of ' v ' in equation (4)

Transverse drive mode : In this arrangement the vibrations of the prongs of the tuning fork are in the direction perpendicular to the length of the string.

The time, during which the tuning fork completes one vibration, the string also completes one vibration. In this mode, frequency of the string is equal to the frequency of the tuning fork.

Therefore from equation (5),

Frequency

Where

The total mass M is equal to the mass M' of the weight in the scale pan plus the mass M0 of the scale pane, M = M' + M₀.

Longitudinal drive mode: In this arrangement the tuning fork is set in such a manner that the vibrations of the prongs are parallel to the length of the string.

The time, during which the tuning fork completes one vibration, the string completes half of its vibration. In this mode, frequency of the fork is twice the frequency of the string.

Frequency

Using equation (6) and (7) we can calculate the frequency of electrically maintained tuning fork in two different modes of vibration.

In transverse drive mode the string follows the motion of the tuning fork, up and down, once up and once down per cycle of tuning fork vibration.

However, 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.

Materials required

Electrically maintained tuning fork, fine thread, scale pan, weights and meter scale.

Procedure

1. Find the weight of pan P and arrange the apparatus as shown in figure.

2. Place a load of 20 to 200 gm in the pan attached to the end of the string.

3. Excite the tuning fork by switching on the power supply.

4. Adjust the position of the pulley so that the string is set into resonant. Vibrations

and well defined loops should be obtained.

5. Measure the total number of the loops ‘N’ formed in the total length of the

string ‘L’ . Hence length of one loop l = L/N

6. Note down the weight placed in the pan and calculate the tension T. (T= Mg)

7. Repeat the experiment for different set of mass.

8. Measure total length of the thread and find its mass using physical balance to

find the mass per unit length ‘µ’.

Observation and Calculations:

For longitudinal arrangement:

Linear density (mass per unit length)

µ = mass of the thread / length of the thread = ………. kg/m

Average Frequency n avg = …………Hz

For transverse arrangement

Linear density (mass per unit length)

µ = mass of the thread / length of the thread = ………. kg/m

Average Frequency navg = …………Hz

Result

The Frequency of vibrations on a string in Transverse arrangement = ---------------Hz

The Frequency of of vibrations on a string in Longitudinal arrangement =--------------Hz

Average value of Frequency of vibrations on a string =-------------Hz

Reference Material

1. Amritha University Virtual Lab: https://vlab.amrita.edu/?sub=1&brch=195&sim=840&cnt=1

2. PHET Virtual Lab: https://phet.colorado.edu/en/simulation/legacy/photoelectric

Questions

1. What is transverse wave?

2. What is longitudinal wave?

3. What are nodes and antinodes?

4. What is linear density?