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Horn-Type Loudspeakers

Horn-type loudspeakers are used extensively where large audiences are to be served, as in a large auditorium or in a stadium. These loudspeakers usually consist of a horn attached to a moving-coil driving unit such as is shown in Fig. 20. The function of the horn is interesting as the following quotation30 indicates.

Figure 20. Cross section of a driving unit for a horn-type loudspeaker. The impedance is about 15 ohms at 1000 cycles, and is largely resistance, a 15° lagging angle being typical. This unit, when coupled to a horn may be driven with approximately 20 watts. The efficiency is about 35 per cent. (Courtesy Racon Electric Co.)

Contrary to the prevalent conception, the horn does not merely gather up the sound energy from the receiver and concentrate it in certain directions. Its relation to the diaphragm is much more intimate. It causes an actual increase in the load on the diaphragm, making it advance against a greater air pressure, and withdraw from a greater opposing rarefaction. Anyone can assure himself that the average sound energy in a room is greatly reduced on removing the horn from a good loud speaker. And frequently when the horn is removed the amplitude of vibration of the diaphragm becomes so great that it strikes against the pole pieces. A receiver element without a horn is analogous to a motor without a connected load; or better yet, a receiver element without a horn is like a closed oscillation circuit from which little radiation takes place (radiation resistance zero); while with a horn it is like an open oscillation circuit with an antenna (radiation resistance considerable). The horn is the antenna of the loud speaker.(1)

The Air Chamber. The horn itself is connected acoustically to the diaphragm by the throat and air chamber as indicated by Fig. 20. This air chamber acts as an acoustic transformer for, owing to the differences between the area of the diaphragm and the area of the throat, a small diaphragm velocity gives the air in the horn a greater velocity and much higher air pressure.30

To explain further the theory of the air chamber and the throat, assume that the volume of the chamber is so small that as the diaphragm is moved forward all the air is forced out instead of being compressed. If the area of the throat is now reduced, it is apparent that, as this area becomes smaller, the mechanical load on the diaphragm grows larger. Thus, if the throat is closed, the diaphragm will be damped, and substantially no motion will be possible when the coil is energized. The size of the area of the throat is made such that the diaphragm is effectively coupled to the air, and the opposition to motion is then almost a pure mechanical resistance.1 For good frequency response, this resistance relation should hold over the entire frequency range. The area of the throat should not be made too small or air friction will be excessive.

Size of the Horn Mouth. If the area of the horn mouth is not correct, sound waves of the lower frequencies will not be effectively radiated from the horn but will be reflected back down the horn.30 As the sound waves suddenly leave the mouth of a horn, the waves greatly increase in volume and decrease in pressure. If the air pressure outside the mouth is lower than that immediately within, the air velocity just within the mouth will be increased. This in turn will cause the pressure just behind to decrease and the velocity to increase. By this action, therefore, sound waves are propagated back down the tube to the diaphragm.

These reflected sound waves represent acoustic power which is not radiated into the air. Also, these reflected waves either aid or oppose the action of the diaphragm, depending on the phase relations they have upon reaching the diaphragm, and hence on their wavelength. This action will result in distortion. Hanna stated31 that such reflections will not be objectionable if the diameter of the horn mouth is greater than one-fourth of the wavelength of the lowest frequency that it is desired to radiate. In horn design, the mouth is given an area approximately equal to the area of a circle having a diameter equal to one-quarter the length of the wave of lowest frequency to be radiated; this applies approximately for rectangular openings.

Rate of Taper. From the preceding discussions it is seen that the area of the throat must be small to load the diaphragm properly, and that the mouth of the horn must be large to radiate the lower frequencies into the air effectively. The next consideration is the shape and length of the horn to connect these two extremities properly,

Wave reflection will occur at any discontinuity. If reflection along the horn is to be minimized, the relative increase in cross-section area should be uniform. Thus, the exponential horn, "whose sectional area varies exponentially with its length",1 is used. This horn is defined1 by the following relations:

where S is the area of plane section of the horn normal to the axis at a distance x from the throat of the horn; S0 is the area of plane section of the horn normal to the axis at the throat; and T is a constant which determines the rate of taper of the horn.

The effectiveness with which an exponential horn transmits sound energy to the mouth is determined by the frequency of the sound wave in relation to the rate of taper, or rate at which the horn opens out, that is, to T, It can be shown30 that, for frequencies below about f = 4000T, the transmission is poor, and, if the frequency is further reduced, a cutoff frequency is soon reached. At high audio frequencies the propagation along an exponential horn is excellent. In the past, conical horns having poor characteristics were used.

Hanna gave a simple rule for laying out exponential horns.31 In such horns the area doubles at equal intervals along the length. Since the cutoff frequency is a function of the rate of expansion, the cutoff is also a function of the length between two circles having a ratio of 2 to 1. As he pointed out, if the area doubles every 3 inches, the cutoff frequency will be 256 cycles; if it doubles in 6 inches, it will be approximately 128 cycles; and if every 12 inches, it will be 64 cycles.

Since the throat area must be small and the mouth opening large, and furthermore since good frequency characteristics demand that the rate of taper be not too large, the exponential horn must be comparatively long. In the open, or where space is not limited, a trumpet horn is sometimes used, the maximum length of such horns being about 6 feet. Where space requirements are important, horns are sometimes coiled, lengths as great as 12 feet having been obtained in this way. At present a folded-horn construction is usually employed. The material used in constructing a horn should be such that portions of the horn do not vibrate or rattle.

Short Exponential Horns.16 The diaphragm of the driving unit of Fig. 20 sends sound waves toward the open mouth of the horn. The air pressure is high at the narrow throat and decreases in intensity as

the wave travels toward the mouth. If a short section of an exponential horn is coupled to a loudspeaker with a large diaphragm, such as Fig, 19 and if this large diaphragm produces the same acoustic pressure at a given point in the short horn as the driving unit of Fig. 20 produces at a corresponding point in a long horn, the performance should be similar.

Short exponential horns with loudspeakers of the general type of Fig. 19 having diaphragms about 6 inches or more in diameter are used as just described. From the discussion given for the long exponential horn with a small throat, it is apparent that the efficiency would not be so high. The frequency response, however, may be excellent, and the directional characteristics are good.

In some instances the horn used with a loudspeaker such as Fig. 19 is very short, often merely a flared system of boards of a variety of shapes. Such arrangements are commonly called directional baffles. They increase the efficiency and directivity but little over that obtained with a flat baffle.



(1) Reprinted by permission, courtesy C. R. Hanna, J. Slepian, and the American Institute of Electrical Engineers.


Last Update: 2011-05-30