EXPERIMENT NO. 303

VELOCITY OF SOUND IN SOLIDS.

References: Stewart, Physics, Sect. 315, 319, 334, 335; Kimball, College Physics, Sect. 288, 335, 342; Duff, College Physics, Sect. 153, 154, 168; Spinney, Text-Book of Physics, Sect. 425, 437, 466.

The method here described is known as Kundt's Method. As in Experiment No. 302, the velocity is found by measuring the wave-length of a sound in the material under test and determining the frequency of vibration.

A glass tube about a meter long and 3 or 4 centimeters in diameter is supported horizontally. A metal or glass rod has a piston made of thin fiber material securely fastened to one end. This piston fits the glass tube fairly closely. The rod is clamped securely at its exact center to the frame supporting the large glass tube so that the fiber piston is held inside the tube some distance. A wooden rod with a cork piston fitting the tube loosely closes the other end of the tube. Some dry cork filings are spread over the space in the tube between the two pistons. When a glass rod, so clamped, is stroked lengthwise with a damp cloth, or a metal rod with a piece of rosined leather, a shrill note is produced by the rod vibrating longitudinally with a node in the middle and a loop at each end. The wave-length in the glass or metal is twice the length of the rod.

We can find the wave-length in air in the following way. Let the length of the air-column be adjusted till one of the overtones of the column is in resonance with the note given out by the rod; the air-column will be set into strong vibrations and there will be nodes and loops distributed along the tube. Wherever there is a loop, the air is strongly agitated, and this agitation causes the cork-dust to be disturbed and piled in little ridges. Hence the nodes and loops are plainly marked, and the wavelength is twice the distance between nodes. It is best to measure the whole length of the air-column when the best resonance is obtained, and divide by the number of segments in the interval. Twice this result gives the wave-length in air. It is interesting to note that while the piston end of the vibrating rod is a loop,

yet the same point is nearly enough a node for the air-column to be considered as one in this measurement.

As the frequencies of the sounds in the rod and air-column are the same, and as velocity divided by wave-length gives the frequency, we may write the proportion:

Make five trials, getting different positions of resonance. Then from the mean result, calculate the velocity of sound in the rod, given that the velocity in air is

V1 = 331001+t/273 cm per second,

t

where t is the temperature of the air on the Centigrade scale. Brass and steel rods are provided. Obtain a set of results with each rod.

EXPERIMENT NO. 304

STANDING WAVES: MELDE'S EXPERIMENT.

References: Stewart, Physics, Sect. 316, 332, 333; Kimball, College Physics, Sect. 323-328; Duff, College Physics, Sect. 146, 165, 166; Spinney, Text-Book of Physics, Sect. 425, 429, 467.

Standing or stationary waves occur when two wave trains having equal amplitudes and wave-lengths travel through the same medium in opposite directions. The following experiment is known as Melde's Experiment. The purpose is to study the formation of standing waves and to find the frequency of an electrically-driven tuning fork.

To one prong of a tuning fork, electrically driven, attach a thread at least two meters long. Pass the other end of the thread, which should be parallel to the prong of the tuning fork, over a pulley and attach a light scale-pan to this end. Now put such weights in the scale-pan as will permit the thread to vibrate in distinct segments. Under proper conditions there are points of the thread which stand still while all points between are vi

brating. This effect, called a stationary wave, is produced by the interference of the waves sent out from the fork, with the waves reflected from the other end of the string where it passes over the pulley. The points of no motion are called nodes, and the distance between two successive nodes is a half wavelength, λ/2.

But the expression for the velocity of a transverse wave in

a string is

Τ

m

where T is the tension of the string and m

is the mass per unit length. Also the velocity, V, of any wave is given by the expression, V-nλ, where n is the number of vibrations per second. Hence, nλ, and therefore n, can be calculated, since A, T, and m can be measured. T is the weight in the scale-pan plus the weight of the pan, reduced to dynes, and m is the number of grams per unit length of the thread. The value of m is obtained by weighing several meters of the thread and dividing the mass by the length.

It is usually easiest to obtain a fairly large number of segments at first by the use of a very small load. Adjust the load carefully till the amplitude of vibration becomes as large as possible. Record the length of the thread from fork to pulley, the number of segments and the total load. Increase the tension. till the number of segments is one less and again record the data mentioned above. Repeat until the number of segments is reduced to three and, if possible, to two. Sometimes the thread will stand enough tension to give one segment. In each case compute n, the frequency of the string. If the thread is parallel to the fork prongs, this number will also be the frequency of the fork, but, if the thread is run at right angles to the prongs, the frequency of the thread is one-half that of the fork. Why?

From a consideration of the formulas and the fact that the frequency of vibration is constant, the student may figure the approximate tension needed to produce any desired number of segments after he knows the tension producing some other number.

Many electrically-driven forks are designed for use with direct current, but, if alternating current only is available, the fork should be weighted so as to have a frequency twice that of the current and there should be no interrupter in the circuit.

EXPERIMENT NO. 305

VIBRATING STRINGS.

References: Stewart, Physics, Sect. 333; Kimball, College Physics, Sect. 326-328; Duff, College Physics, Sect. 165, 166; Spinney, Text-Book of Physics, Sect. 467.

The purpose of this experiment is to test the laws of vibrating strings by means of a sonometer and a set of tuning forks. The pitch of a string is given by the formula,

where T is the tension in dynes (found from the weight hung on the wire, plus the weight of the scale-pan), L is the length of the vibrating string, and m is the mass per centimeter length of the string. We may put this into a form that is more directly applicable to the measurements taken from the apparatus as follows:

m = Tr2d.

where r is the radius of the string and d the density of the metal. Therefore, we may write the main formula,

This formula states that the frequency varies (a) inversely as the length of the string; (b) directly as the square root of the tension; (c) inversely as the square root of the mass per unit length of the string.

The sonometer is a sounding box arranged so that strings can be stretched over it by means of weights, and the lengths of the vibrating portions of the strings can be changed by adjustable

bridges. Too little tension means that the string will rattle, and also that the vibrating length for a given note will be short; while too much tension may break the string. As a rule, not less than four kilograms should be used, nor more than eight. In order to avoid too short vibrating lengths, it will also be wise to choose forks of not more than 512 vibrations per second. Forks giving tones of the major chord are preferable.

Stretch a thin brass or steel wire on the instrument with suitable tension, and by means of the movable bridge tune it to unison with one of the forks of known frequency. The preliminary tuning must be done purely by ear, but when the wire and fork are nearly in agreement, beats may be heard if the fork is struck and the stem held against the sounding board, and at the same time the string is plucked. Tuning should be continued till these beats are eliminated as nearly as possible. Another method will sometimes be of service. If the string and fork are in unison, the string may be set in vibration by the sound waves coming from the fork. Hence, if a small slip of paper is made into the form of a V and set on the wire, and the stem of the vibrating fork is rested on the top of the sonometer, the wire will be set vibrating and the rider agitated or thrown off, provided the wire is properly tuned. It is a very common error to tune the string an octave below the tuning fork. In this case, however, a rider at the middle of the string will not be disturbed, while others nearer the ends will be violently agitated.

If the first law is true, the lengths of the wire giving unison with the various forks multiplied by the frequencies of the forks will give a constant value. Test this relation for three or four forks, recording the results.

The second law may be tested as follows: The load on one wire is first set at 8 kgm and then at 6 kgm, and the wire tuned in each case to the same fork by means of the bridge. The formula shows that if n and m are not varied, then the square root of T divided by L should be a constant. Test this relation.

The third law may be tested by using a brass and a steel wire or two steel wires of different sizes. Put equal tensions on the wires and tune them to the same fork by shifting the movable