Waves Character of Explosions
by Fred Scaffidi, Chemist
The concept of a wave is useful in describing many different phenomena in nature. Water waves, sound waves, radiation (which has a wave character) and blast waves have vastly different effects on their respective environments however, they all have properties in common. I find these properties quite descriptive of the character of waves.
One of the most fundamental concepts in chemistry and physics is that of the energy of a system. Recall from your basic physics that if a small stone is held at a certain height and allowed to drop it will strike the ground with a certain energy. This energy is called "kinetic energy" and is calculated to be 1/2mv2 where "m" is the mass of the stone and "v" is the velocity on impact with the ground. The energy of the stone is converted to several possible forms on impact such as heat and sound. If the ground is soft, energy can be used in compression. Similarly if one strikes a nail with a hammer the nail heats up indicating that not all energy went into driving the nail but some was lost to heat caused by friction. The term system is used to refer to the objects and environment in question. The stone and the ground are the system in our case. A glass beaker containing hotly reacting chemicals is an example of a system releasing energy to the surroundings as heat. Energy is a property which can be measured and is assigned a unit called Joules (J). The heat of a substance is a specific form of energy measured in calories (1 calorie = 4.186 J). A calorie is defined as the amount of energy required to raise the temperature of 1 gram of water by 1°C and is the preferred unit when talking about heat energy.
All compressed gases possess a property called "energy". If one reacts acetylene gas and oxygen in a welders torch, there is a tremendous amount of energy released in the form of heat. The energy contained within the acetylene and oxygen are released to the surroundings (the flame temperature can get as high as 3700°C). A burner releases energy gradually while as we all know acetylene explosions can occur if the explosive limits (2.5% to 80% in air) are attained. An explosion occurs when there is an instantaneous release of energy from a system to the surroundings.
Lets look at the case where our stone is dropped into a pool of water. The energy of the stone causes a disturbance in the water and waves are generated. These waves appear as a series of crests and troughs. The energy imparted to the water by suddenly "pushing" it is transmitted. If one takes a look at water waves from a side view, one would see a picture similar to the one below:
The crest of the wave or its height is referred to as the amplitude of the wave. The length of the wave is its wavelength as shown. The wavelength is the distance for one complete positive and negative phase to complete, i.e. a cycle. A stone generates many cycles and the number of cycles generated per second is the frequency. Dropping a stone into a pool of water will generate many circular waves, not simply one large wave. The amplitude of the waves will diminish to zero with time as energy is lost to the water. The greater the amplitude of the wave, the more powerful or intense. If a high amplitude wave travels to a wall barrier, it will be reflected back or if it is powerful enough it will simply knock the wall down.
A typical wavelength in a tank of water is on the order of 1 cm. The water is the medium through which energy is transported and this medium has certain mechanical properties, such as viscosity (how easily the liquid flows) and elasticity which dictate how waves travel through it; the water particles themselves are actually moving up and down, perpendicular to the direction of motion of the wave. (Actually, they may follow a circular motion which appears to be just an up/ down motion.) You can see this by placing a cork on the water in the path of the waves. The cork will bob up and down but will not move in the direction of wave motion.
Sound represents another type of wave. When we speak our vocal chords vibrate and impart energy to the air. Waves are generated and transmitted through the medium. Sound waves are a series of compressions and rarefactions (crests and troughs) of air. These high and low pressure zones are detected by our eardrums as sound. Sound waves differ from water waves in that the wavelengths involved are much shorter. They also travel at a much greater speed (331 m/s) in air and a sound frequency can be as high as 109 cycles/s. As mentioned earlier, the medium involved has an effect on the propagation of waves. Sound energy can be transmitted through other media and result in different wave speeds. Sound waves travel at 1450 m/s in water while sound through iron travels at 5130 m/s. The rigidity of iron seems to aid in the propagation of sound and illustrates that the nature of the medium certainly has an effect on the way waves propagate. Sound cannot be transmitted in the absence of a medium i.e., vacuum. Waves can be reflected off of objects as well.
An explosion in air will similarly release energy to the surroundings. Just as with the stone falling into the water, an explosion will provide a push of the surrounding air. This push is provided by the hot expanding gases generated by the explosive. The amplitude of the wave is actually referred to as the over pressure in air when speaking of explosions. What might the wave profile look like in this case? See below:
A high explosive such as dynamite will release its energy instantaneously. This instantaneous release will result in a shock wave of great amplitude (over pressure) and short duration. In addition the wave speeds in a detonation have been shown to be supersonic. Indeed, we normally use the word detonation to mean cases in which the wave speed is supersonic. Being supersonic, the wave over pressure can strike an individual before the sound from the explosion has had a chance to arrive. There is also a zone of slightly negative pressure that follows a detonation and is caused by the forward momentum of the air. Many explosions involving compressed gases are not detonations but rather extremely rapid deflagrations, that is to say the shock waves travel at subsonic speeds and the over pressure peaks are lower. Although over pressures are lower, deflagrations can still cause damage as they generally are longer in duration. As the medium involved has been shown to be important, we can speculate that an explosion in the vacuum of space would be less destructive than a similar explosion on earth.
The waves discussed so far fall into a broad class which are best described as mechanical waves. What about radio waves, light waves and other types of radiation? These waves are electromagnetic in nature, that is they involve fields of energy. These waves travel at the speed of light (3 x 108 m/s). A typical visible light wavelength can be approximately 10-6 m. The wave energy is better thought of not as a series of compressions or overpressures but in the form of small bundles of energy which have both particle and wave character. Light travels through many media without affecting the media but is easily stopped by an opaque object. X-rays are highly energetic waves (wavelength 10-9m) which pass through many materials and are useful in medecine. Radio waves and microwaves travel extremely long distances and through many materials without being weakened or disturbed. These waves are used to communicate with satellites and deep space probes many kilometers distant. Radiation from a nuclear explosion is hazardous as a broad spectrum of radiation is generated which strikes the human body and passes through it doing tremendous damage to human cells. Electromagnetic waves need to be looked at somewhat differently as they possess extremely short wavelength and travel at the speed of light. They don't require a medium for transmission. They can be reflected just as other types of waves.
The concept of a wave is a recurring theme in nature. It is one of the ways in which energy is transmitted from a system to its surroundings. The energy concept is also useful as it allows for an accounting of the events of nature. A particular system has a constant amount of energy which can be converted from one form to another. If we can predict how energy is distributed during explosions for example, we can prepare ourselves for the potential consequences.
Publication: TDG Dangerous Goods Newsletter, Vol. 17, No. 1, Spring 1997.
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