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by a dimming of the polished surface) read the thermometer placed in the water, and immediately remove all unmelted ice. Stir vigorously until the film of moisture on the outside of the cup disappears and again read the thermometer. The average of the two readings is the dew-point. Repeat the above operations three times, take the average of the three sets of readings, and call this the true dew-point of the air in the room. Care should be taken not to breathe on the cup during the experiment. Why? Also, if the dew-point is near the room temperature it is easy to add too much ice, and time is lost in waiting for the film to disappear. In this case it is well to add very small pieces of ice, or better, a little cold water.
If the dew-point is very low, it may be necessary to use salt with the ice.
Having determined the dew-point and the room temperature, look up humidity tables and find the relative humidity. Such tables are found in: Smithsonian Physical Tables; Smithsonian Meteorological Tables; Physical and Chemical Constants, by Kaye and Laby; D. C. Miller, Laboratory Physics; Stewart, Physics, page 296.
(b) Wet-and-dry-bulb method. If the vapor present is not saturated, water will be evaporated continually. A thermometer with its bulb covered with a thin layer of wet cotton will read lower than one with a dry bulb. Hang two thermometers side by side, one dry and the other with bulb covered with wet cotton. Let stand for some time till the reading of the wet-bulb instrument becomes steady. Record the two values. Tables and graphs have been prepared which give the relative humidity when the air temperature and the wet-bulb temperature are known. These can be found in some of the works mentioned under (a), and in Measurements for the Household, Circular of the Bureau of Standards, No. 55. If the two thermometers are mounted on a frame which may be whirled in the air, we have the sling-psychrometer. The tables to be used if the air is thus forced rapidly past the thermometers differ somewhat from those for use if the air is still.
The relative humidity as determined by the two methods, (a) and (b), should agree fairly closely. In a large laboratory it is often true that the humidity will be quite different in different parts of the room, especially when the windows are closed and the heating system is in action.
WAVE MOTION AND SOUND
EXPERIMENT NO. 301
References: Stewart, Physics, Sect. 310, 311, 314, 316; Kimball, College Physics, Sect. 274-279, 292-294, 324; Duff, College Physics, Sect. 140, 141, 144-147; Spinney, Text-Book of Physics, Sect. 421, 424-427, 429.
Knowledge of the fundamental principles of wave motion is essential to an understanding of the phenomena of sound and light and of certain phases of electricity. The type of wave most commonly seen is the surface wave in water. Many of the simpler wave phenomena can be made visible by the use of water waves, and the underlying principles can be made clear. The student should keep in mind, however, that the waves by which sound, light, or electrical energy are transmitted are not of this type at all and he should be careful not to make too sweeping generalizations from these experiments.
A wave trough with plate-glass sides is needed. This trough should be about 200 cm long by 10 cm wide by 25 cm deep. The wooden parts should be made waterproof and the joints carefully sealed with paraffin. Some sawdust, a paddle, and a foot of No. 14 bare wire are also needed.
(a) Shallow water waves. The dependence of speed on depth will first be tested. Measure the inside length of the trough with a meter stick. Then fill the trough to a depth of about one centimeter. With the paddle, or better by lifting one end of the trough slightly, start a single wave, which will travel back and forth being reflected at the ends of the trough. Measure the time required for the wave to make say six round trips; and from the observed time and measured distance compute the speed of the wave. Repeat the observations for accuracy. In this work, do not try to follow with your eye the wave as it
goes back and forth, but keep your attention on one end of the trough, where the arrival of the wave is easily seen by the sudden rise of the water. In the manner described get the speed of waves for depths of 2, 3, 4, 5, 6, 7, and 8 cm; and, if there is time, for greater depths.
From your data, compute the ratio of the speed to the square root of the depth and show that this ratio is constant for all the depths used. Compare your value for this constant with the theoretical value, obtained from the equation, V = √g d, where g is the acceleration due to gravity and d is the depth of the water. Is the speed of these waves dependent on wave-length?
(b) Particle motion. Drop some coarse saw-dust into the water and see to it that some of the particles are below the surface. Have the water about 10 cm deep. Send out a few short, high waves with the paddle and watch the paths pursued by the particles as the first waves go by, before the reflected waves begin to return. Describe the paths of the particles near the surface and near the bottom. Repeat the tests until you are sure. It should be clear that the particles have a motion quite distinct from the motion of the wave-form down the trough.
(c) Interference; standing or stationary waves. With the paddle deep in the water, send out a steady train of waves of constant frequency. By trying a few times a frequency will soon be found for which the water will appear simply to move up and down, without any appearance of horizontal motion. These waves are the stationary waves which result from the interference of the original and reflected trains of waves. Different numbers of loops can be obtained by changing the frequency. Observe the nodes between the loops. Are nodes or loops found at the ends of the trough? On account of this necessary condition at the ends of the trough, what must be the relation between the wave-length and the length of the trough?
(d) Deep water waves cannot be produced satisfactorily in the laboratory and must be observed outside when the opportunity offers. The speed of such waves is given by the equation;
where A is the wave-length, and g the acceleration due to gravity, S the surface tension, and d the density of the liquid. For long waves the last term of the radical is of no importance, but for ripples the last term is the decisive one in determining the speed, for in this case the wave-length is very small.
With the water quite deep in the trough, draw a piece of wire through the water and observe the train of very fine ripples formed just ahead of the wire. Try the effect of moving the wire faster and slower. Does an increase in speed lengthen or shorten the wave-length of the ripples? Does this agree with the indications of the equation? Would the effect be the same for long waves?
EXPERIMENT NO. 302
VELOCITY OF SOUND IN AIR.
References: Stewart, Physics, Sect. 315, 319, 328, 336; Kimball, College Physics, Sect. 287, 290, 338; Duff, College Physics, Sect. 153, 155, 167 168; Spinney, Text-Book of Physics, Sect. 425, 437, 449, 460-462.
It is seldom feasible for a laboratory section to determine the velocity of sound in air by measuring the time required for a sound to traverse a known distance. An indirect method of measuring the velocity requires the determination of the wavelength in air of a sound of known frequency. The velocity is the product of the frequency and wave-length. A tuning fork, whose pitch is known, gives vibrations of a definite frequency. If an air-column can be adjusted to resonance with the fork, the wave-length of the sound can be measured.
The apparatus consists of a vertical glass tube, 3 to 5 centimeters in diameter, the lower end of which is attached to a water reservoir by means of a rubber tube. The water level in the tube may be changed by raising or lowering the reservoir. Raise the water to a level within a few centimeters of the top of the tube. Strike the tuning fork with a rubber hammer, and hold it over the mouth of the tube with the prongs vibrating vertically; then lower the water level and listen carefully. When the water is at a certain level, the sound of the fork will become
much louder because each sound-wave from the fork is reflected from the water surface and returns to the top of the tube at the right instant to reenforce a new wave just starting out. In other words there is a node at the water surface and a loop just above the top of the tube, and the length of the air-column is practically one-fourth of a wave-length of the sound. According to the theory of closed pipes, resonance will again occur when the air-column has a length of three-quarters of a wave-length and again at five-quarters, etc. The distance between any two successive resonance levels is one-half wave-length.
Mark with suitable indicators the positions of the water surface which cause resonance and measure the lengths of the air-columns above these levels. Make four or five trials at each level and record all measurements. With care, the trials should not differ by more than two or three millimeters. Compute the wave-length of the sound. Record the frequency number which is stamped on the fork. Multiply the frequency by the wavelength to obtain the velocity of sound at the existing temperature. Find the temperature by suspending a thermometer in the tube for three or four minutes. Reduce the value of the velocity thus found at the room temperature to that at the freezing point by the formula,
Find the velocity of sound at 0° C by this method, using three different forks.
Ear-pieces like those of a stethoscope may be attached by a rubber tube to a side-tube near the top of the resonating column or to a short U-tube hung over the upper edge of the resonator. Such a listening device tends to eliminate outside noises and aids in the determination of the resonance levels.
It should be noted that the shortest resonating air-column is not exactly one-fourth wave-length as the loop is not at the exact top of the tube. The nodes, however, are accurately one-half wave-length apart. In finding the average wave-length therefore, only the differences between lengths of air-columns should be used; never the length of the shortest air-column.