Amplitude can also be controlled by varying the shape of the acoustical tooling components. The basic unit of ultrasonic tooling, the horn, sonotrode, or coupling bar, is in its simplest form when it is a cylinder of metal, typically aluminum, titanium, or hardened tool steel, that is a half wave long and less than 1/3 wave in diameter. Wavelength drives tooling proportions, so the size of a tool with comparable running characteristics will vary in inverse proportion to wavelength– low frequency tools will be larger than high frequency tools. A straight cylinder will simply transmit amplitude unchanged through its length, but not by moving in piston fashion. The vibration enters one flat face of the cylinder which is driven in reciprocal fashion by the working face of the transducer or converter. This reciprocal motion drives the cylinder in to half-wave resonance. The simmplest way to describe this is to say the two flat faces of the cylinder move in opposite directions while the diameter at the midpoint of the length of the cylinder gets larger and smaller. This elastic motion is easy to visualize if you consider the cylinder as having two masses at each end joined by a spring in the middle. If the frequency of the motion exactyl matches the spring rate, the two masses will move in opposite directions in repeating fashion, in other words, the item will resonate. The reason we refer to this as a half wave is that the two ends of the device move in opposite directions, and the midpoint stands still. This point where there is no motion is referred to as a node, or nodal point. Now, if the cylinder is not a simple cylinder but has different diameters on each side of the nodal plane, the ampltude will be different at either end of the device. According to the law of conservation of momentum, the end with lower mass will move at higher amplitude than the end with higher mass. Thus, a booster is a half-wave component that either increases or decreases ampltiude according to its shape (or it may be a device which does not change amplitude at all!). If there is more mass on the input end than the output end, the booster will increase amplitude and vice versa. Any tool, even one not specifically called a booster will exhibit this characteristic. The difference in ampltiude between the ends is referred to as gain. Gain is expressed as a ratio, and common practice, at least in the US, is to refer to a device than increases amplitude in terms of its output amplitude compared to its input amplitude. Thus a device which doubles amplitude is referred to as having a gain ratio of 2:1, pronounced “two to one.” This means of expressing gain is often reversed in Europe, so the same device would be said to have a gain ratio of 1:2, or “one to two.” The reverse of this device would by common parlance be referred to as having gain of 0.5:1 or 1:0.5, so this difference in usage is less confusing than one might otherwise expect. Some manufacturers have dropped the “…to one” part of the ratio, and simply refer to gain as being 2.0 if the device doubles amplitude or 0.5 if it halves it. Bear in mind that a booster is designed for operation with a specific input end and output end, and may not be used as a booster with opposite gain ratio by simply swapping ends, as tuning will be compromised if this is done.