On the Nocturnal Increase in the Intensity of Sound.

By M. de Humboldt.

From the Annales de Chimie et de Physique.

THE increase in the intensity of sound during the night, is a problem which is not resolved in any of the works on natural philosophy.

I shall endeavour to give a solution derived from the latest researches on the theory of sonorous undulations; but before treating of the cause of this phenomenon, I shall mention the circumstances under which it takes place.

It has been remarked from the earliest antiquity that the intensity of sound increases during the night.

Aristotle has spoken of it in his Problems, and Plutarch in his Dialogues. It is only the increase of sound when the air is calm that we are now treating of, not that which accompanies a change of wind in the night, and which is modified by the relation that exists between the direction of the wind, and that of the sonorous ray.

Under the same latitude (between the tropics for example), the nightly increase of sound has appeared to me greater on the plains than on the heights of the Andes, 3000 metres above the level of the sea; and also, when on a low level, more considerable in the middle of continents than in the open sea.

This estimation is founded on the comparative noise of two volcanos, that of Guacamayo, and of Cotopaxi, which I have frequently heard both by day and by night, one in a level plain between the city of Quito and the savannahs of Chillo, and the other on the Pacific Ocean, ten leagues west of the coast of Peru.

The roarings of the volcanos of the Cordilleras usually succeed each other with great uniformity every five minutes: they are not attended with any visible explosion above the edges of the craters; and resemble, sometimes distant thunder, at other times, repeated discharges of heavy cannon.

In places in which the ground is covered in winter with snow in the vicinity of cascades, it would be interesting to examine whether the nocturnal increase of sound is not less in winter than in summer, when the soil is strongly heated by the rays of the sun.

It is to be observed, that in what I have mentioned of the difference between the daily and nightly sound from sonorous objects in the high and low levels of South America, I only consider the comparative intensities under the same barometric pressure.

I do not compare the absolute intensity at different altitudes, but the difference between the diurnal and nocturnal intensity on high levels and on plains.

The variation of absolute intensity observed at different heights of the atmosphere, is a problem which the mathematical theory of sound has long resolved. M.

Poisson has even arrived at this remarkable result, that the intensity of sound from below upwards or from above downwards, whether the sonorous rays are propagated vertically or obliquely, depends only on the density of the stratum of air whence the sound has proceeded.

One must not therefore confound totally distinct problems.

When the noise of the great cataracts of the Orinoco is heard, at more than a league distance, in the plain that surrounds the mission of Alures, the observer thinks he is close to a coast surrounded with reefs and breakers.

The noise is three times as great by night as by day, and gives an inexpressible charm to those solitary regions.

What can be the cause of this nocturnal increase of sound in a desert, in which nothing seems to break in upon the silence of nature?

The diminution of temperature, so far from increasing, would retard the velocity of sound.

The intensity of sound diminishes in a wind blowing in an opposite direction: it also diminishes by the expansion of the air; it is weaker in the higher than in the lower regions of the atmosphere, where the particles of the agitated air have more density and more elasticity in the same ray.

The intensity is the same in a dry air as in one full of vapour, but it is weaker in carbonic acid than in the mixtures of azote and oxygen.

On considering these facts (the only ones that we know with certainty), it is difficult to explain a phenomenon which is observed near every cascade, and has been the subject of common remark both in Europe and in America.

Near the Orinoco the temperature of the air is lower by about five degrees (Fahrenheit) by night than by day; whilst the visible moisture increases at night, and the haze round the cataracts becomes denser.

We have just seen that the hygroscopic state of the air has no influence on the propagation of sound, whilst the velocity of the latter is diminished by the cooling of the atmosphere.

It might be supposed that, even in places remote from the habitation of man, the buzzing of insects, the singing of birds, and the rustling of leaves in the gentlest winds, produce, by day, a confused noise; which, being uniform, may fill the ears without materially distracting the attention, and thus imperceptibly lessen the effect of any louder sound.

But this reasoning, whatever be its force, can hardly apply to the forests of the Orinoco, when the air is constantly filled with an innumerable multitude of moskitoes, so that the buzzing of insects is much stronger by night than by day; and where also the breeze, when it occurs at all, springs up after sunset.

I am inclined to think, that the presence of the sun affects the propagation and intensity of sound by the obstacles opposed to its transmission by currents of air of different densities and partial undulations, the result of the unequal heating of various parts of the earth's surface.

In air at rest, whether it be dry, or mixed with elastic vapours equally distributed through it, the sonorous undulation is propagated without difficulty.

But when this air is crossed in every direction by small currents of a warmer temperature, the sonorous undulation divides into two waves, at the spot where there is the most sudden change in the density of the medium; thus producing partial echoes, which weaken the body of sound, because one of the sonorous waves is reflected back upon itself.

The theory of these partitions of sonorous waves has been lately explained by M. Poisson, with the intelligence which distinguishes all his labours.

. It is not, therefore, the motion of the passage of the particles of air from below upwards, nor the small oblique currents of this fluid that we consider as opposing, by impulse, the propagation of the sonorous waves.

A stroke or impulse impressed on the surface of the liquid will form circles around the impinging centre, even when the liquid is in agitation.

Several kinds of waves may cross in air, as well as in water, without interfering with each other; but the true cause of the less intensity of sound in the day time appears to be the want of homogeniety in the elastic medium.

There is at this time a sudden change of density throughout, produced by small currents of air, of a high temperature, rising from portions of the earth's surface that are unequally heated.

The sonorous waves are then divided in the same manner as luminous rays are refracted, and form a mirage of sound wherever strata of air of unequal density are contiguous.

A distinction must be kept between the intensity of sound or of light, and the direction of the sonorous or luminous wave.

When these waves are propelled across strata of different densities two simultaneous effects will be produced, there will be a change in the direction of the wave, and extinction of light or sound.

The reflexion that accompanies each refraction weakens the intensity of light; the separation of the sonorous wave causes partial echoes, and that portion which returns on itself becomes insensible to our ear, in weak noises, at the spot where the density of the medium suddenly changes.

Annales de Chimie, T. 7.

In the mirage with double images, that which has undergone refraction contiguous to the earth is always weaker than the direct image.

Strata of fluids, of very different density, may so alternate, that the primitive direction of the luminous or the sonorous ray will remain the same, but the intensity of the ray will be not the less weakened on that account.

During the night the surface of the earth cools; the parts covered with grass, or with sand take the same temperature; the atmosphere is no longer crossed by currents of hot air, rising obliquely or vertically in every direction.

The medium being now become more homogeneous, the sonorous wave passes with less difficulty, and the intensity of sound increases, as the separations of the sonorous waves and echoes become less frequent.

To give a precise idea of the cause of these currents of hot air, which rise in the day-time from a soil unequally heated; I will mention some observations which I have made under the Tropic.

In the Llanos, or steppes of Venzuela, I have found the sand at two o'clock heated to 126° Fahrenheit, and sometimes as high as 140°. The air under the shade of a Bombax was 97°; in the sun, eighteen inches from the ground, 109°.

At night the sand was only 82°, having lost at least 46°.

Near the falls of the Orinoco, the ground being covered with grasses, its temperature rose in the day only to 86°, that of the air being 79°, but at the same time the temperature of beds of granite lying on the surface was 118°. I have published a great number of similar observations in my account of experiments on the mirage at Cumana, at the same period that Dr. Wollaston was employed on the same subject in Europe.

If I have given the true cause of the nightly increase of sound, it will not be surprising that, under the torrid zone, this increase is greater within land than on the open sea; greater in the level plains than on the sides of the Cordilleras.

The surface of the equatorial seas heats uniformly, and not beyond 85° Fahrenheit, whilst that of the continents, being variously coloured, and composed of materials of very different powers of radiation, acquires a heat of from 86 to 126°.

Under the tropics the earth usually remains warmer during the night than the air: in the temperate zones, on the other hand, in calm nights, the surface of the ground cools down to seven or eight degrees below that of the air.

In Europe, the temperature, instead of diminishing as the distance from the ground recedes, presents a regular progressive increase to the height of fifty or sixty feet.

It is not surprising, therefore, that the terrestrial refractions are sometimes in the temperate zone almost as great by night as by day.

There will always be strata of air, of different densities, resting horizontally one upon the other; but the streams of warm air that cross the atmosphere obliquely, will be more rare at night than in the day.

At 3000 metres in height, in that part of the Andes which is situated beneath the equator, the mean temperature of the air is only 57°, and the force of radiation towards a cloudless sky, through a dry and very pure air, hinders the soil from heating considerably in the day time.

I shall not dwell farther on these local circumstances, it is sufficient to have made the general deduction of the nocturnal increase of sound from the theory of sonorous undulations and their divisions.

The whole depends on the want of homogeniety in the vertical columns of the atmosphere, which (according to the ingenious application that M. Arrago has made of the interference and neutralisation of the rays) is also the true cause of the scintillation of the stars.

Besides, it is well known that the propagation of sound is sensibly altered when a stratum of hydrogen gas is made to rest above one of common air, in a tube closed at one extremity.

The mountaineers of the Alps, as well as those of the Andes, regard an unusual increase of sound in calm nights as a sure prognostic of a change in the weather.

"It is about to rain," say they, "for the noise of the torrent comes nearer." M.

Deluc has endeavoured to explain this phenomenon by a change in barometric pressure, and by an increased number of bubbles of air breaking on the surface of the water.

This explanation is forced, and but little satisfactory.

I will not attempt another hypothesis, but I will suggest the analogy that exists between the prognostic derived from an increase of sound, and from that of light.

The inhabitants of the mountains also expect a change of weather, when, in calm weather, the mountains covered with snow appear suddenly to approach nearer to the observer, and when their outlines are unusually well defined upon the blue sky that surrounds them.

Whatever be the constitution of the atmosphere that causes these appearances, it is not a little curious to observe in it a new analogy between the motions of the sonorous and the luminous undulations.