Physics Lab Manual PDF

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BASIC PHYSICS LAB MANUALS FOR

Undergraduate Classes

DEPARTMENT OF PHYSICS

UNIVERSITY OF ENGINEERING AND TECHNOLOGY, LAHORE, PAKISTAN

Experiment 1

Title To determine the frequency of A. C. Mains by Meld’s

Page . 2

Experiment 2

To determine the resolving power of diffraction grating.

13

3

To determine the Modulus of rigidity of material of a

21

wire by Maxwell needle. 4

To determine the elastic constant Modulus of rigidity of

30

the material of flat spiral spring 5

To determine the velocity of sound by resonance method.

39

6

To determine the specific heat of solids.

44

7

To find the variation of photoelectric current with

51

intensity of light. 8

To find e/m of electron by Deflection Method .

56

Experiment # 1 To determine the frequency of A.C. mains by Meld’s Experiment.

Objective: Calculate the frequency of A.C. mains by Melde’s experiment through transverse arrangement.

Equipment Details: i.

Electric vibrator (solenoid, electric bulb, soft iron rod, permanent magnet)

ii.

Thread and pulley

iii.

Chemical balance

iv.

Meter scale

v.

Weights

Experimental Setup:

Figure 1: Experimental setup for generating standing wave pattern.

An electric vibrator consists of a solenoid whose coil is connected to A.C. mains. The circuit includes a high resistance in the form of an electric bulb as shown in Fig1. A soft iron rod AB is placed along the axis of the solenoid, clamped near the end A with two screws X and Y while the end B is free to move. The rod is placed between the pole pieces of a permanent magnet NS. One end of the thread is attached to the end B and the other passes over a frictionless pulley and carries a weight. When an alternating current

is passed in the coil of the solenoid, it produces an alternating magnetic field along the axis. The rod AB gets magnetized with its polarity changing with the same frequency as that of the alternating current. The rod AB vibrates n times per second due to interaction of the magnetized rod with the permanent magnet. . The tension in the string can be varied by placing different weights in the pan, stationary waves are produced due to the superposition of the direct waves sent by the strip and reflected waves from the pulley.

Procedure: i.

Take a uniform thread of one meter long and attach its one end to the point B of the rod and the other to a light pan by passing it over a frictionless pulley.

ii.

Place an electric vibrator in the transverse position.

iii.

Find the mass of one meter long thread through chemical balance and then calculate mass per unit length. It is denoted by ‘m’.

iv. v.

Connect the A.C. mains to the solenoid of an electric vibrator. Fix the pulley and switch on the A.C current so that it passes through an electric vibrator. Thus the changing magnetic field produces vibrations in the rod.

vi.

Add small weights in the pan such that the string vibrates in one loop with maximum amplitude under the forced vibrations of the rod.

vii.

Note the tension T(=weight of the pan + weights added) and measure the length l of the loop. By reducing the tension, the string is made to vibrate in two, three, four loops and so on. viii.

Note the number of loops p formed in the length L of the thread. This gives the value of l as

ix.

l = L/p.

Calculate the frequency of A.C. mains by using formula.

Observations and Calculations: Mass of the empty scale pan m1 =……………………gms Length of the thread =……………………………..cm Mass of the thread =………………………………gms Mass per unit length of thread= m=……………….gms/cm

No. of

No. of

Distance

Length of

Mass

Mass of

Tension in

Frequency of

obs.

loops N

between

each loop

added to

pan

the thread

A.C. mains

two

l =L/N

the pan

m1+Mass

T=Mx981

m2

added m2

extreme nodes L (cm)

M=m1+m2 (cm)

(gms)

(gms)

1

2

3

Mean frequency f =……………… (Hertz)

Standard result: Frequency of A.C. mains = ...... cycles/sec. Percentage error = ...... %

Result: The frequency of A.C. mains, using. Transverse arrangement = ...... cycles/sec.

Applications:

(dynes)

(Hz)

i.

Alternating current (AC) electricity is the type of electricity commonly used in homes and businesses throughout the world. AC electricity alternates its direction in a back-and-forth motion. The direction alternates between 50 and 60 times per second, depending on the electrical system of the country.

ii.

The AC electricity can be readily transformed to higher or lower voltage levels. High voltages are more effecient for sending electricity at great distances, high voltages from the power station can be easily reduced to a safer voltage for use in the house. Changing voltages is done by the use of a transformer. This device uses properties of AC electromagnets to change the voltages.

iii.

Tuning of instruments like guitar.

iv.

Standing waves in air coloumn.

Sources of error and precautions: i.

Pulley should be frictionless.

ii.

The loops formed in the thread should appear stationary.

iii.

Do not put too much load in the pan.

iv.

Pass the current for a short time.

v.

vi.

Take accurate measurements of length and mass. Do not apply DC power to this instrument. DC current will NOT cause the rod to vibrate and a larger than normal current may flow. This could cause excess heat and eventual damage to the instrument.

Theory: A wave is the propagation of a disturbance through a medium. The physical properties of that medium (e.g., density and elasticity) will dictate how the wave travels within it. A wave may be described by its basic properties of amplitude, wavelength, frequency and period T. Figure 2 displays all of these properties. The amplitude, A, is the height of a crest or the depth of a trough of that wave. The wavelength λ is the distance between successive crests or successive troughs. The time required for a wave to travel one wavelength is called the period T. The frequency f is 1/T, and is defined as the number cycles (or crests) that pass a given point per unit time.

Figure2: Properties of waves Since the wave travels one wavelength in one period, the wave velocity is defined as. The λ/T wave velocity can then be written as

when a vibrating body produces waves along a tightly stretched string, the waves are reflected at the end of the string which cause two oppositely traveling waves to exist on the string at the same time. These two waves interfere with each other, creating both constructive and destructive interference in the vibrating string. If the two waves have identical amplitudes, wavelengths and velocities, a standing wave, or stationary wave, is created. The constructive and destructive interference patterns caused by the superposition of the two waves create points of minimum displacement called nodes, or nodal points and points of maximum displacement called antinodes. If we define the distance between two nodes (or between two antinodes) to be L, then the wavelength of the standing wave is λ=2L. Figure 3 illustrates the case where the length of string vibrates with 5 nodes and 4 antinodes.

Figure 3. A standing wave is created when an incident and reflected wave have identical amplitudes, wavelengths and velocities. It is possible to obtain many discrete vibrational modes in a stretched string. That is, for a string to vibrate with a specific wavelength, the tension applied to the string must have a certain value. It is possible for the string to vibrate with another specific wavelength, but the tension must be adjusted until that

particular mode is reached. If the tension is such that it is between vibrational modes, the string will not exhibit the standing wave phenomenon and we won't see a standing wave. When the frequency of the vibrating body is the same as that of the particular vibrational mode of the string, resonance is established.

Speed of transverse wave in stretched string: A string means a wire or a fibre which has a uniform diameter and is perfectly flexible i.e.which has no rigidity. In practice, a thin wire fulfills these requirements approximately. The speed of transverse wave in a flexible stretched string depends upon the tension in the string and the mass per unit length of the string. Mathematically, the speed v is given by

Where T is the tension in the string and m is the mass per unit length of the string. When a wire clamped to rigid supports at its ends is plucked in the middle, transverse progressive waves travel towards each end of the wire. These waves are reflected at the ends of the wire. By the superposition of the incident and the reflected waves, transverse stationary waves are set up in the wire. Since the ends of the wire are clamped there is a node N at each end and a anti-node A in the middle.

We know that the distance between two consecutive nodes is λ/2 , where λ is wavelength. Hence if l be the length of the wire between the clamped ends, then l = λ/2 or λ=2 l. If f be the frequency of vibration

of the wire, then f = v/λ= v/2 l Substituting the value of v, we have

.

VIVA VOCE Q. 1. What do you mean by A.C. mains? Ans. A current which changes its direction of flow i.e. continuously varying from zero to a maximum value and then again to zero and also reversing its direction at fixed interval of time. If a graph of the current against time has the form of a sine wave, the current is said to be sinusoidal Q. 2. What is the frequency of your A.C. mains? What does it represent? Ans. The number of times the current changes its direction in each second is called the frequency of A.C. mains. It’s value is 50 cycles per second. Q. 3. What do you understand by resonance? Ans. In case of forced or maintained vibrations, when the frequencies of driver and driven are same then amplitude of vibration of driven becomes large. This phenomenon is called resonance. Q. 4. Does direct current also have any frequency? Ans. No, it does not change its direction. Q. 5. How does the iron rod vibrate? Ans. When alternating current is passed through the solenoid, the iron rod is magnetized such that one end is north pole while other end is south pole. When the direction of current is changed, the polarity of rod is also changed. Due to the interaction of this rod with magnetic field of permanent magnet, the rod is alternately pulled to right or left and thus begins to vibrate with frequency of A.C. mains. Q. 6. What type of vibrations does the rod execute? Ans. The vibrations are forced vibrations. The rod execute transverse stationary vibrations of the same frequency as that of A.C. Q. 7. Can you use a brass rod instead of soft iron rod? Ans. No, because it is non-magnetic. Q. 8. How is it that by determining the frequency of the rod, you come to know the frequency of A.C. mains?

Ans. Here the rod vibrates with the frequency of A.C. mains. Q. 9. What is the construction of an electric vibrator? Ans. It consists of a solenoid in which alternating current is passed. To avoid the heating effect in the coil of solenoid, an electric bulb is connected in series. A rod passes through the solenoid whose one end is fixed while the other is placed in pole pieces of permanent horse shoe magnet. Q. 10. What are resonant vibrations? Ans. If the natural frequency of a body coincides with the frequency of the driving force, the former vibrates with a large amplitude. Now the vibrations are called as resonant vibrations. Q. 11. When does resonance occur? Ans. When the natural frequency of the rod becomes equal to the frequency of AC mains, resonance occurs. Q. 12. Define Transverse waves? Ans. The vibrations in which the particles of the medium vibrate in a direction perpendicular to the direction of wave motion are called as transverse vibrations or waves. Q. 13. Define Stationary waves? Ans. A stationary wave is formed when two identical waves travelling in the same medium but coming from opposite direction superimpose. Q. 14. What types of waves are set up on the thread? Ans. Transverse standing waves are set up on the thread. Q. 15. What are node and anti-node points? Ans. When a standing wave is set up in a medium, those points which are at rest and do not vibrate are called nodes. Those points which vibrate with maximum amplitude are called antinodes. Q.16. What is the distance between two consecutive nodes or antinodes? Ans. It is λ/2. Q.17. What does Melde’s experiment demonstrate? Ans. It demonstrates the formation of stationary waves.

EXPERIMENT#2 To determine the resolving power of diffraction grating Apparatus: Spectrometer, sodium lamp, diffraction grating, slit of adjustable width with scale, spirit level. Diagram:

Figure 1: Schematic view of a Spectrometer using a diffraction grating. Procedure: 1) Look through the telescope at any light-colored surface and push the eyepiece in and out until the cross-wires can be seen sharply, without straining the eyes. 2) Focus the telescope onto a distant object (may be a wall at far end of lab) by adjusting knurled knob only, until a sharp image of object is seen and there is no parallax with the cross-wires. The telescope is now focused for a parallel light – do not change this focus. 3) Switch on the sodium lamp and place it up against the collimator slit. 4) Position the telescope at the “straight-through” position (see Fig. 1) i.e. where it is pointing directly at the collimator to observe the image of the slit through the telescope. 5) Adjust the discharge lamp position in relation to the slit to obtain the brightest possible image. Focus the collimator by adjusting the knurled knob only, until a sharp image of the slit is observed on the cross-wires. 6) Reduce the width of the collimator slit using the adjusting screw (see Fig. 1) until a fine vertical unbroken line is seen. The collimator will now be producing a beam of parallel light and the telescope is focusing it onto viewer’s eye. Do not make further adjustments of telescope or collimator. 7) Ensure that the central mounting table is fixed to the main turntable, and is at a suitable height, by means of the single screw on its shaft. Using a spirit level and the three screws underneath, adjust the table until it is absolutely level. Check it remains level as the main turntable is rotated.

The spectrometer should now be in good adjustment.

Determination of resolving power 1) Set up the grating along with the adjustable slit on the central mounting table and fix it with the screw at appropriate height with respect to collimator and telescope. 2) Open the adjustable slit to its maximum with the help of side screw. 3) Set the telescope for straight through image of collimator’s slit. 4) Move the telescope to right and observe the first order spectrum of sodium light. The two sodium D-lines will appear separated by a dark line. 5) Reduce the slit width by closing the side screw by observing at the spectrum through telescope until the two sodium lines appear just to merge into one. 6) Note the width of slit by taking the reading from scale on side screw of the adjustable slit. 7) Close the slit completely and start opening it until the single sodium line splits into two Dlines. Note the width of the slit. 8) Repeat the observation for first order at left side and then for second order on both sides. 9) Record the observations in the table and perform necessary calculations. 10) Determine the resolving power of diffraction grating using the formula R.P = mN where

m = order of spectrum N = number of lines in the opened width of adjustable slit

Observations and Calculations: Groove density N = No of lines engraved per mm of diffraction grating = 600 Grating element d = 1/ N = 1/600 (mm) = …………. mm Width of the slit when the D lines Order of Sr. No.

Just Merge

Just Separate

Mean Width

Spectrum w1

w2

w=(w1+w2)/2

m (mm) 1.

1(Right)

2.

1(Left)

3.

2(Right)

(mm)

(mm)

No. of lines in the opened width N=N×w

Resolving Power R.P = mN

4.

2(Left)

Mean resolving power =

Results: Determined resolving power of diffraction grating = Actual Resolving Power = λ/dλ = 5890/6 = 982 for first order Percentage Error = Actual – Experimental Actual Theory/Related Concepts: a) Spectrometer Spectrometer is an instrument use to study the spectra. It consists of three major parts. Collimator: A collimator may consist of a curved mirror or lens and an adjustable slit to control the amount of light entering the system. Object or light source is placed at the focus of optical assembly. The purpose is to replicate a target at infinity. The light to be analyzed enters the collimator through a narrow slit. The light leaving the collimator is therefore a thin, parallel beam, which ensures that all the light from the slit strikes the diffracting element at the same angle of incidence. This is necessary if a sharp image is to be formed. Turn table: It is served as a platform for diffracting/dispersing medium (a prism or diffraction grating). The diffracting element bends the beam of light. If the beam is composed of many different colors, each color is diffracted to a different angle. Telescope: An astronomical telescope is used to focus the parallel rays coming from the infinity. This telescope can be rotated to collect the diffracted light at very precisely measured angles. With the telescope focused at infinity and positioned at an angle to collect the light of a particular color, a precise image of the collimator slit can be seen and measurements can be made.

Figure 2: Spectrometer diagram.

b) Optical resolution It describes the ability of an imaging system to resolve detail in the object that is being imaged. Resolution depends on the distance between two distinguishable radiating points. Several standards are used to determine, quantitatively, whether or not the points can be distinguished. The Rayleigh criterion is the generally accepted criterion for the minimum resolvable detail. The imaging process is said to be resolved when the first diffraction minimum of the image of one source point coincides with the maximum of another.

Figure 3 (a) Two sources are far apart, and the patterns are well resolved. (b) The sources are closer together such that the angular separation just satisfies Rayleigh’s criterion, and the patterns are just resolved. (c) The sources are so close together that the patterns are not resolved. c) Sodium Lamp The sodium spectrum is dominated by the bright doublet known as the Sodium D-lines at 588.9950 and 589.5924 nanometers. From the energy level diagram it can be seen that these lines are emitted in a transition from the 3p to the 3s levels. The line at 589.0 has twice the inten...