THE PHYSICS 11
LAB BOOK
Book 2: Labs 20 – 38
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TABLE OF CONTENTS
SOUND
20...... Standing Waves on Strings – Electric Tuning Fork 51
21...... The Velocity of Sound in Air – Air Column Resonance 53
22...... The Velocity of Sound in Metals 55
MAGNETISM AND ELECTRICITY
23...... Magnetic Field Plotting 57
24...... Electric Field Plotting 59
25...... Ohm's Law – Series and Parallel Circuits 61
26...... Kirchhoff's Rules 63
27...... AC Circuits and Resonance 65
28...... The Magnetic Field of the Earth – Tangent Galvanometer 69
29...... The Potentiometer 71
30...... The Wheatstone Bridge 73
31...... The Heating Effect of an Electric Current 75
LIGHT
32...... Reflection and Refraction – The Optical Disk 77
33...... The Thin Lens – Convex and Concave Lenses 79
34...... The Thin Lens – Optical Instruments 83
35...... Reflection and Refraction at Plane Surfaces 85
36...... Spectral Lines 89
RADIATION PHYSICS
37...... Radiation Detectors – The Geiger Counter 91
38...... Radiation Absorption 93
The Statistics of Measurement
The Least-Squares Fit to Data
Experiment 20
STANDING WAVES ON STRINGS
Electric Tuning Fork
INTRODUCTION
In this experiment the relationship between the tension in a stretched string and the wavelength of the standing waves produced in it will be investigated.
Standing waves are produced by the interference between two traveling waves with the same wavelength, velocity, frequency and amplitude traveling in opposite directions. The equation for the velocity of propagation of transverse waves on a stretched string is:
where T is the tension in the string and is the linear density (the mass per unit length of the string). The velocity of propagation v, the frequency of vibration f, and the wavelength are related this way:
v = f
A stretched string has many modes of vibration. It may vibrate as a single segment, in which case its length is half of a wavelength. It may vibrate in two segments with a node (zero displacement) at the center as well as at each end; then the wavelength is equal to the length of the string. The wavelengths of the many modes of vibration are given by the relation:
where L is the length of the string, is the wavelength, and n is an integer called the harmonic number.
EQUIPMENT & MATERIALS
Electric tuning forkHeating coilThick string
StroboscopeRuler4-inch "C" Clamp
Electronic balanceMeter stickSlotted masses
Battery chargerLeads & connectorsRod pulley table clamp
Rod pulley50-gram mass hangerScissors
2 caliper jawsDouble-wall calorimeter
EXPERIMENTAL PROCEDURE
1.Cut off a piece of string about 2 meters long and determine its length, mass and linear density.
2.Clamp the apparatus to one end of your table and clamp the pulley to the other end, as shown in Figure 1. Clamp the string to one end of the tuning fork and knot the other end to the mass hanger. Suspend the string over the pulley, and adjust the pulley until the string is horizontal. Record the mass of the mass hanger. /Fig. 1: Standing Waves on Strings Apparatus
3.Connect the positive terminal of the battery charger (set at 6 volts) to one tuning fork terminal, connect the other tuning fork terminal to the heating coil and calorimeter filled with water (used to decrease the tuning fork’s amplitude), and connect the other terminal of the heating coil to the negative terminal of the battery charger, as shown in Fig. 1. Set the fork into vibration by adjusting the contact point screw above and to the left of the two terminals of the tuning fork apparatus, while tapping the tuning fork to make it vibrate.
4.Measure the frequency of the tuning fork by using a stroboscope. Start with the strobe frequency set at 4000 cycles per minute, and lower it until one stationary image of the tuning fork is obtained. When lowering the frequency of the strobe, also observe that a stationary image is obtained when the strobe frequency is ½, ⅓, ¼, etc., times that of the tuning fork. Divide the number that appears on the stroboscope by 60 to get the frequency of the tuning fork in cycles per second (Hertz).
5.Vary the tension of the string by adding masses to the hanger until the string vibrates in five segments with maximum amplitude. Switch to the 12-volt setting if the vibrations are too small to see easily. Measure the length of one segment from a point vertically over the center of the pulley wheel to a node (zero amplitude), to the nearest millimeter by sliding two caliper jaws over the meter stick. The wavelength will be twice the length of one segment. Record in the data table the added mass in kilograms. Then record the total mass m (added mass plus the mass hanger) in the data table. Record the resulting tension T = mg in Newtons, with g = 9.80 m/s/s.
6.Repeat the procedure for 4, 3 and 2 segments by adding more mass to the pulley.
7.Compare the experimental velocity (v = f) with the theoretical velocity () by computing the percent difference. When you have finished the experiment, empty the calorimeter, and dry it thoroughly.
Experiment 21
THE VELOCITY OF SOUND IN AIR
Air Column Resonance
INTRODUCTION
The resonance of sound waves in air columns will be used to determine the velocity of sound in air. This is accomplished by producing standing waves in air in closed pipes using sound of a certain frequency.
If a tuning fork is set into vibration and held over an air column, compressions and rarefactions in the air travel down the tube and are reflected at the closed end of the tube with a change of phase of 180o. If an integral number of quarter wavelengths just fit into the tube, a condition called resonance occurs and the loudness of the note from the tuning fork is increased. The lengths of tube for this resonance condition are given by: L1=(1/4), L2 = (3/4), L3= (5/4, and so forth, as shown in Figure 1 below.
Fig. 1.
The position of the antinode at the open end of the tube is just outside the end of the tube. This small, extra distance is called the "end correction", e, of the tube and is proportional to the diameter of the tube. Theoretically, the end correction should be approximately equal to 0.30 times the diameter of the tube. The actual lengths of the resonating air column for the first three resonance conditions are given by:
(1/4)= L1 + e(3/4) = L2 + e(5/4) = L3 + e
from which: = 2(L2 - L1),or = 2(L3 - L2),or = (L3 - L1) .
The value for the end correction e of the tube is given by : e = .
In this experiment, the length of a pipe, closed at the bottom, is varied by changing the level of the water in the reservoir as shown in Figure 2. The apparatus consists of a plastic tube about a meter long mounted vertically on a tripod stand with a rubber hose connecting the lower end of the tube to the movable reservoir. A tuning fork is held close to the top of the tube with the prongs vibrating vertically.The relation between the velocity of sound in air, the frequency of the wave, and the wavelength is v = f. The velocity v can be calculated if the frequency f is known and the wavelength is measured. /
Fig. 2.
EQUIPMENT & MATERIALS
Resonance tube2 tuning forks, 450 Hz Rubber mallet
Thermometer 600 ml beakerMetric ruler
EXPERIMENTAL PROCEDURE
1.Fill the reservoir when it is lowered all the way to the bottom of the apparatus. Then adjust the water level in the resonance tube by raising the reservoir until the water level is about 10 cm from the top of the tube.
2.Strike the tuning fork with the rubber mallet and hold the tuning fork horizontally over the top end of the resonance tube about 1 cm above the tube so that the prongs vibrate vertically, as shown in Figure 2. Lower the level of the water in the resonance tube by lowering the reservoir tank and record the position when resonance is first heard. (Watch out for harmonics; you should hear a definitely augmented note.)
3.Repeat the procedure two more times for a total of three independent trials and record the data in the table.
4.Repeat steps 2 and 3 for the second position of resonance. This will be a distance of ½ lower down the tube.
5.Repeat steps 2 and 3 for the third position of resonance. You may need to drain some water from the apparatus to obtain a large enough value of L3.
6.Repeat the experiment for the second tuning fork with a different frequency.
7.Calculate values of wavelength, velocity of sound v = f, and the end correction e. Determine an average value for the velocity of sound.
Theoretically, the velocity of sound in air in units of meters per second is v=331.7 + 0.607 T, where T is the ambient temperature of the air in degrees Celsius. Calculate this theoretical value, and determine the percent difference from your own value.
Calculate an average of your values of the end correction e. Theoretically, e=k(diameter of pipe) where k is a constant of proportionality. Calculate your value of k, and compare it to the theoretical value of 0.30.
8.Drain and dry your equipment as thoroughly as possible.
Experiment 22
THE VELOCITY OF SOUND IN METALS
INTRODUCTION
This acoustic tube apparatus was used historically to find the velocity of acoustic (longitudinal) waves in metals by using the known velocity of sound in air. Its use in this laboratory experiment is to give some direct laboratory experience in measuring the velocity of acoustic waves in solids in the form of metal rods.
The theoretical velocity of a compressional wave in a metal is given by the following relation:
v = .
where Y is the Young's modulus and is the density. Take this value of the velocity to be the theoretical value for computing the percent difference.
For aluminum:Y = 7.0 X 1010 N/m2, = 2700 kg/m3
For steel:Y = 19.2 X 1010 N/m2, = 7800 kg/m3
For brass:Y = 9.2 X 1010 N/m2, = 8400 kg/m3
The velocity v, frequency f, and wavelength , are related by: v = f
The velocity of sound in air varies with the temperature in degrees Celsius as:
v = (331.7 + 0.607 T) m/s
where T is the temperature in degrees Celsius.
EQUIPMENT & MATERIALS
Acoustic tube apparatusThermometerCotton rag
Metal rods (aluminum, steel, brass)Meter stickRosin
2 Caliper jawsCork stopper
EXPERIMENTAL PROCEDURE
1.Clamp the rod exactly at its center, that is, at its length L/2 as shown in the Figure 1.
2.Spread the bottom of the length of the tube with a fraction of a teaspoon of cork dust (a little goes a long way), and place a cork stopper at the far end of the tube.
Fig. 1. Experimental Apparatus
3.Stroke the rod with a rosined cloth using single straight strokes parallel to the rod. With the proper technique, you should get intense vibrations and the cork dust will gather in a pattern showing compressions and rarefactions. The position of the tube itself can be adjusted lengthwise to produce the best standing wave patterns in the cork dust. The tube may also be rotated slightly after the stroke to show the pattern more clearly on the side.
4.The standing waves in a column of air create an alternating series of nodes and antinodes. At each antinode the air vibrates horizontally, pushing the cork dust away. The distance between antinodes is half a wavelength. Select one antinode, and measure the distance from the antinode on its left to the antinode on its right (see Fig. 1). This equals the wavelength in air, air. Use caliper jaws on the meter stick to measure this as accurately as possible.
5.Calculate the frequency of the sound in air f = vairair. Since the air vibrates because the rod vibrates, this must equal the frequency of the sound waves in the rod.
6.The center of the metal rod is a node (it can’t vibrate) and the ends are antinodes. Therefore, the wavelength of the sound in the rod (rod) is twice the length of the rod. Calculate the velocity of sound in the rod, and compare it to the theoretical value by computing the percent difference.
7.Repeat the experiment for the two other rods.
Experiment 23
MAGNETIC FIELD PLOTTING
INTRODUCTION
A compass is a small horizontal magnetized needle pivoted around its center, permitting the needle to point in the direction of the Earth’s magnetic field. A magnet is a bar of metal (usually iron) that has been magnetized, creating a magnetic field around it. The magnetic field of a bar magnet can be pictured as exiting the bar at its north magnetic pole, curving around the outside of the bar magnet and re-entering at its south magnetic pole. A bar magnet in the presence of the Earth’s magnetic field creates a single magnetic field that is influenced by both sources. In this experiment, you will use the compass to trace out the magnetic field generated by the Earth and the bar magnet.
EQUIPMENT & MATERIALS
Magnetic compassPlywood boardMeter stickColored pencils
11 X 34 drawing paperFrench curve Bar magnetMasking tape
EQUIPMENT & MATERIALS FOR THE INSTRUCTOR DEMONSTRATION
2 sheets of large drawing paper5 horseshoe magnets4 bar magnets
5 Plexiglas sheetsIron filings
EXPERIMENTAL PROCEDURE
1.Place the plywood board between tables so as to minimize interference from the metal bar underneath each table. Place a large sheet of paper on the board for plotting the points on the magnetic field lines.2.Determine the direction of magnetic north by placing the compass on the sheet, and making sure that no magnets are within a five-foot radius of the compass. Orient the board and paper as shown in Figure 1, so the Earth’s magnetic field runs approximately parallel to the short side of the paper. Place /
Fig. 1.
an arrow in the direction of magnetic north on one corner of the paper, and have all the members of your lab group print their names there. Place a bar magnet on the west edge of the paper, oriented as shown in Figure 1. Trace its outline, and label its poles as ‘N’ and ‘S’. Place eight dots at 10-cm intervals between A and A.
3.Place the center of the compass on the dot nearest the magnet, and make dots as near as possible to each end of the needle with a pencil. Move the compass needle so one of these two dots is now under the center of the needle. Make another dot at the forward end. Continue in this fashion, following up from the previous dot and working both ways from the original dot, until either the magnet or the end of the paper is reached. Use the French curve to connect all dots for the line with a smooth curve.
4.Repeat step 3 for the other seven dots, using different colors for each magnetic field line.
5.Move the compass from A to A, until it seems to rotate aimlessly when tapped, or else points perpendicular to magnetic north. It will take some careful observation to locate the best point. At this point, the magnetic field of the magnet cancels the horizontal component of the magnetic field for the Earth, which is approximately one-fourth gauss or 0.000025Teslas. Label this point as the neutral point.
6.Each of the eight magnetic field lines on your paper should have an arrowhead pointed from the white end to the red end of the compass needle. If there are any large blank areas on the paper near the magnet, place the compass there and trace out additional magnetic field lines. There should be enough field lines that you can estimate the direction of the magnetic field everywhere on the paper.
7.Turn your paper over, then place a bar magnet on the north edge of the paper, as shown in Figure 2. Trace its outline, and label its poles as ‘N’ and ‘S’. Place eight dots at 10-cm intervals between B and B, and between C and C. Repeat steps No.3 to No. 6 to find the magnetic field lines through the dots. Find the neutral point between points A and A. /Fig. 2.
For the instructor; classroom demonstration.
Place magnets of various types under a sheet of clear Plexiglas, and scatter iron filings on top. Tap the plate until the filings show the shape of the magnetic field clearly. Try these combinations:
a) horseshoe magnet;
b) two parallel bar magnets with north poles adjacent;
c) two parallel bar magnets with south and north pole adjacent;
d) two horseshoe magnets with unlike poles facing each other about 5cm apart;
e) two horseshoe magnets with like poles facing each other about 5 cm apart.
Experiment 24
ELECTRIC FIELD PLOTTING
INTRODUCTION
In this laboratory exercise we will determine the configuration of the electric field lines between electrodes of various shapes which are held at a constant potential. This is accomplished by plotting a set of equipotential lines (lines of equal voltage), and then constructing the lines of the electric field which are at right angles to the equipotentials.
Each equipotential line is constructed from a set of equipotential points which are located by means of the movable probe of the digital voltmeter. The four lines at potentials of 2, 4, 6, and 8 volts are drawn and used to determine the configuration of the electric field.
EQUIPMENT & MATERIALS
Electric field plotting apparatus4 banana wiresRuler
Hewlett-Packard multimeter2 alligator clipsPlain paper
3 sheets of electrode paperFrench curveCarbon paper
DC Regulated Power Supply
EXPERIMENTAL PROCEDURE
1.Starting with the dipole electrode configuration (two silver circles), arrange the apparatus as shown in Figure 1. To do this, place the plain paper on top of the cork board, place the carbon paper black-side down on the plain paper, and place the electrode paper on top. Take two pins and the two thin wires inside the electric field plotting apparatus, and firmly pin one end of each wire to an electrode. The other end of each should be grasped by an alligator clip connected to a wire, which is in turn plugged into the DC Regulated Power Supply set between 10.0 volts and 12.0 volts. Traditionally, red signifies the positive side and black is the negative side. The electrodes are now charged, and have established an electric field across the electrode paper.