Sound volume, sensitivity and speaker output

Sound is waves propagating in air, that is, fluctuations in air pressure. As you know, the unit of pressure measurement is pascal, in these units the sound pressure is measured, which corresponds to the amplitude of the sound wave.

Sound waves carry energy and can be characterized by the power flux density (that is, the energy carried by the sound wave through a unit area perpendicular to the direction of propagation) per unit time. Let’s first answer the question, what is sound volume?

Sound volume it is a subjective quantity that characterizes the idea of ​​sound intensity.

The loudness of a sound depends in a complex way on the sound pressure (or sound intensity), duration, and also the vibration frequency or sound spectrum.

How do you connect all these values?

The answer can be found by delving into old reference books and magazines and translating non-systemic units into the SI system. The results are summarized in table. 3.1:

Table 3.1 Loudness, sound pressure and power flow

Volume, dB	Sound characteristic	Sound pressure, Pa	Power flux density, μW / m2
0	Hearing threshold	2 × 10-5	ten-6
ten	Quiet whisper at a distance of 1 m	6.4 x 10-5	ten-5
twenty	Rustle of foliage	2 × 10-4	ten-4
thirty	Whisper at a distance of 1 m	6.4 x 10-4	0.001
40	Quiet conversation at a distance of 1 m	0.002	0.01
50	Poor loudspeaker performance	0.0064	0.1
60	Normal conversation at a distance of 1 m	0.02	1
70	Loud loudspeaker operation	0.064	ten

The table is compiled according to the data of the reference book G. G. Ginkina for a frequency of 1000 Hz clearly audible to the ear. Note that an increase in volume for every 10 dB (the same subjective increase) is caused by a 10-fold increase in the power flow, therefore, at high volumes, the required power rises very quickly.

If we take the distance to the loudspeaker equal to 1 m, as is usually done in acoustic measurements, and assume that the radiation is non-directional, we can also calculate the acoustic power emitted by the loudspeaker simply by multiplying the power flux density by the area of ​​a sphere with a radius of 1 m (remember that exactly the power flux for radio waves was calculated).

For the last three cases shown in the table and of practical interest to us, the radiated acoustic power will be 1.26, 12.6, and 126 μW, respectively.

The required electrical power can be found by dividing the acoustic power by the loudspeaker efficiency. This is where tears begin! For typical low power consumer speakers, it is, in order of magnitude, about 1%. Then we get an electrical power of the order of units of milliwatts.

Electromagnetic loudspeakers (the design of which resembles a telephone), widespread in the early years, have now fallen into disuse due to poor performance and have been replaced by permanent magnet electrodynamic heads. Their output directly depends on the magnetic induction in the gap where the voice coil is located. Heads with a small gap and a strong magnet have high recoil.

Drivers’ datasheets often provide mean standard sound pressure (recoil). It is measured at a distance of 1 m with an electrical power supply of 100 mW and fluctuates, for most types of loudspeakers, in the range from 0.1 to 0.4 Pa. There are reports of heads emitting up to 0.6 Pa. It is curious to calculate what electrical power is needed in this case to obtain a sound volume of 60 dB. The results are shown in table. 3.2.

It can be clearly seen even from this small selection that for our purposes we need loudspeakers with high output, that powerful speakers have more output, and small-sized speakers from pocket and portable receivers are least suitable. The acoustic design of the speaker has a huge impact on the output.

Table 3.2 Recoil of common loudspeakers

Loudspeaker type	Recoil, Pa	The required power of the AF signal for loudness of 60 dB, mW
0.025GD-2	0.075	3.6
0.05GD-1	0.15	1.8
1GD-5, 1GD-28, 1GD-36, 2GD-7	0.2	1.0
1GD-4, ZGD-1.4GD-4, 4GD-5	0.3	0.45
5GD-1.6GD-1 RRZ, 6GD-3	0,4	0.25
8GD-1 RRZ	0.45	0.2

High-quality acoustic systems with an abundance of absorbing material have a return from 0.08 Pa (25AS-16, 25AS-416) to 0.11 Pa (35AS-2), therefore, are of little use.

For imported speaker systems, sensitivity is often indicated – the volume level at a distance of 1 m when an electrical power of 1 W is applied. It usually ranges from 87 to 92 dB. If we reduce the sound volume by some decibels, then the required electrical power will also decrease by the same decibels. It is very easy to calculate that to obtain the required volume of 60 dB, the required signal power 34 should be 27-32 dB less, that is, from 2 mW to 0.63 mW.

Horn loudspeakers have greater efficiency and, accordingly, three times more efficiency, firstly, due to better matching of the electromechanical system with the environment and, secondly, due to some directionality of the radiation. This is confirmed by the amateur radio experience, starting from the 1920s, when there were many reports in magazines that an earphone placed in a glass or on the bottom of a saucepan sounds louder, and descriptions of all kinds of horns made of paper, cardboard and plywood, to ours days, when (very rarely) descriptions of very successful speaker designs with great impact still appear.

A horn acoustic system with a phase inverter rolled into a “horseshoe”, according to the inventors and developers, provided an efficiency of about 2.3% with a 6GD-1 loudspeaker, and even up to 3.4% at low frequencies. Since to obtain a sound loudness of 60 dB, 12.6 μW of acoustic power must be emitted, this system will require 12.6 / 3.4% = 0.56 mW to operate at this loudness.

It seems that the authors somewhat underestimated the efficiency of their speaker, since the 6GD-1 head with standard acoustic measurements on a large screen requires slightly less power and, therefore, has a higher efficiency.

So, we have established that with a highly sensitive speaker, for example with an eight-watt speaker of the Riga Radio Plant 8GD-1 RRZ in a large-volume case, we have enough AF signal power of about 0.2 mW, and with a poor one, for example, with a small speaker from a pocket receiver in a plastic box , and 3 mW will not be enough. Agree, the difference is significant.

Source: amfan.ru