In the case of an open organ pipe,

2 L per vibration = L length of pipe,

and when the pipe is stopped,

4 L per vibration = L length of pipe.

EXAMPLES.

Ex. 1. Water is diminished 1/21000 of its bulk by an additional atmosphere of pressure. Find the modulus of compressibility. 1/21000 ▼ decrement per V = atmosphere additional, 21000 atmospheres = V per V,

i.e.,

or

76 x 13.6 gm. weight per sq. cm. = atmosphere; 21000 × 76 × 13.6 gm. weight per sq. cm. = V per V,

2-16 × 107 gm. weight per sq. cm. = V per V.

21.6 gm. weight per sq. cm. = 10-6 V decrement per V.

Ex. 2. The velocity of sound being 33300 cm. per sec. at 0° C. and 760 mm. pressure; what is it when the temperature is 25° C. and the pressure 745 mm. ?

It is independent of the change of pressure.

333002 (cm. per sec.)2 = 273 deg. Cent.,

273+25 deg. Cent.,

Ex. 3. The mass of a cubic foot of wrought iron is 480 lbs. The velocity of sound in an iron bar is 17,000 feet per sec. Find the force required to elongate an iron bar of one square inch sectional area by 1/10000 of its original length.

Let the modulus be

μ lb. by ft. per sec. per sec. per sq. ft. per (ft. inct. per ft. origl.);

the density is 480 lb. per cubic foot; therefore (Art. 240) the velocity of sound along the bar is

Hence

170002 × 480 poundals = sq. ft. by (ft. per ft.),

Or at a place where gravity is 32.2 ft. per sec. per sec.,

Ex. 4. Calculate the lowest number of vibrations per second of a pianoforte wire 6 feet long, oz. to the foot, stretched by a tension of 10 lbs. weight.

The line-density is

The stretching force is

10 × 32.2 lb. by ft. per sec. per sec.;

.. the velocity of the disturbance along the wire is

i.e.,

Now

√10 × 32·2 × 4 × 16 ft. per sec.,

8√322 ft. per sec.

2 ft. per vibration = ft. wire,

EXERCISE LI.

1. The velocity of sound in air at 0° C. is 333 metres per second; what is it at 27° C.?

2. One o'clock is signalled by a time-gun, at what time will the signal be heard by a person at the distance of one mile, the temperature being 70° F.?

3. Assuming the velocity of sound in air to be 1,120 ft. per sec., determine the length of the wave produced in air by a tuning-fork which vibrates 384 times per second. Determine also the length of an open organ pipe which would yield the same note as the tuning-fork.

4. The length of the column of air which resounds most freely to a given tuning-fork is 32.2 cm.; if the velocity of sound in air be 33,000 cm. per second, determine the frequency of the fork.

5. Find the number of vibrations made in a second by an organ pipe 16 ft. long, open at both ends, sounding its fundamental note, the velocity of sound in air being 1,100 ft. per sec.

6. When the velocity of sound in air is 1,100 ft. per sec., how many vibrations per second are made by a closed organ pipe 4 feet long, sounding its fundamental note?

7. Calculate the frequency of an open organ pipe 3 ft. long sounding its fundamental note, when the temperature is such that the velocity of sound is 1,092 ft. per sec. By how many would the frequency be increased by a rise of temperature of the air to the extent of 2.74 deg. Cent.

8. A pianoforte wire, 5 ft. long, which weighs 14 lbs. per nautical mile, is stretched with a pull of 100 lbs. Find the number of vibrations made per second when it is sounding its lowest note.

9. Supposing, at any particular time and place, the pressure of the atmosphere to be 14 lbs. to the square inch, and a cubic foot of it to weigh 536 grains, and the intensity of gravity to be 32.2 ft. per sec. per sec., what would be the velocity of sound in air, there and then, according to Newton's rule.

CHAPTER EIGHTH.

OPTICAL.

SECTION LII.-PHYSICAL.

ART. 243.-Light. The term light may be used in two senses; first, as equivalent to radiant energy; second, to denote that species of radiant energy which affects our organs of vision. Both of these quantities are properly measured in terms of W, the unit of energy, or rather, in terms of W per T, the unit for current of energy. In measuring the subjective quantity it is difficult to give proper weight to the preference exercised by the organs of vision for particular kinds of radiation.

ART. 244.-Intensity of a Source. Suppose that we have a single source of light placed in a homogeneous medium, and that it is sending forth a constant current

μ W per T.

The light will be propagated in straight lines and equally in all directions. Suppose a spherical surface drawn round the source, having the source for centre. Any small portion of this surface will be cross-sectional to the direction of the current at the place, and the whole amount of cross-section is given by (Art. 87)

4 S cross-section per (L distance)2.

The total current crossing this surface is the same as that emitted by the source, provided none of the light is absorbed by the

medium. Hence the current per unit of cross-section at unit distance, or the intensity of the source at unit distance is given by μ/4 W per TS cross-section per (L distance)2,

ART. 245.-Illuminating Power. By the illuminating power of a source of light is meant the relative intensity as judged by the human organs of vision. If two sources emit the same kind of light, that is, light of the same colour, their illuminating powers are strictly comparable. The comparison is commonly effected by finding the distances at which they produce equal illuminating effects as judged by the eye.

When two sources emit white light, their illuminating powers are also comparable, and the more so the greater the agreement in composition of the two lights.

ART. 246.-Standards of Light. Hitherto it has been the custom to measure illuminating power by means of a standard source. The English standard source is a sperm candle burning 120 grains per hour, six of the candles weighing one pound. The French standard source is a Carcel burner; it is equal to 9.3 standard candles.

The Paris Congress of Electricians appointed a committee to report on a standard of light, and recently the following standard was adopted. The unit of each kind of simple light is the quantity of light of the same kind emitted in a normal direction by a square centimetre of surface of molten platinum at the temperature of solidification. The practical unit of white light is the quantity of light emitted normally by the same source.

ART. 247.-Luminosity; Brightness. The luminosity of an incandescent surface may be defined as the amount of current of light emitted per unit of surface.

The brightness of an object is estimated by the light received