Sound Pressure

     and System Power

Sound loudness, specifically sound pressure, is measured in decibels (dB). The decibel scale is relative and always referenced to a certain value (human hearing threshold, device maximum capability, etc.). The decibel scale can have both positive and negative values. Positive decibels indicate an increase in sound intensity compared to the reference value, while negative decibels indicate a decrease in sound intensity compared to the reference value.

The decibel scale is logarithmic, meaning that every 10 dB increase corresponds to a tenfold increase in sound intensity. For example, if the sound level increases by 10 dB, the sound intensity becomes ten times greater. Similarly, if the sound level increases by 20 dB, the sound intensity becomes one hundred times greater. The commonly used 3 dB in technical specifications corresponds to a doubling or halving of sound intensity.

However, it's not a cause for concern if, for example, a speaker's frequency fluctuates by +/- 3 dB. In psychoacoustics, there is a concept known as the "just noticeable difference" (JND), which represents the smallest change in sound volume that an average listener can perceive. In most cases, the JND value is about 1 to 3 dB. If a speaker has a +/- 3 dB frequency range with no significant anomalies, it creates a smooth response (compared to what the listening environment does to sound).

In some cases, dB is used to express relative noise level. For example, if the main sound level is 80 dB and the harmonic frequency level is 40 dB, it may initially seem very disturbing, as if half of the volume is harmonics. However, in reality, the harmonic frequency's sound intensity in this example is 10,000 times lower than the main sound.

Excessive loudness can damage hearing. The auditory system is highly sensitive and can sustain damage from prolonged or repeated exposure to loud sounds. High sound pressure can harm the eardrum, inner ear hair cells, and auditory nerve. Noise-induced hearing damage is typically gradual, and initially, there might be a decrease in hearing sensitivity for higher frequencies. If exposure to loud sounds continues, it can lead to permanent hearing damage, including reduced hearing across a broader frequency range. The level of hearing damage depends on the sound's pressure and the duration of exposure. Certain sound levels increase the likelihood of hearing damage. Prolonged exposure to sound levels above 85 decibels (dB) can be harmful. Short-term exposure to very loud sound, such as above 120 dB, can also cause damage.

However, listening to music too quietly is not advisable either. Different parts of music have varying volumes. In short, the optimal sound pressure for listening to music is around 70 - 75 dB. During studio monitoring, a sound pressure level of 80 - 85 dB is recommended. Room sound levels can be measured, even with mobile applications. However, with headphones, nobody measures this, and in a small enclosed space, the sound pressure behind the earcup can become very high.

A simple and essential rule for music listening is to keep the sound as low as possible while still allowing for clear audibility of music details and avoiding frequent adjustments to the volume. In practice, a measured and recommended range of 70-75 dB provides the best detailed listening experience in real-life scenarios. Nonetheless, the quieter, the better, as our music is noise pollution to others (not necessarily due to the choice of music, but how sound spreads beyond the listening area). Avoid increasing sound pressure to mask other noises.

Now, the most important question: how powerful of a speaker system do I really need? It's impressive to have a 400 W system, but is it practical? To answer this, several aspects need consideration.

The first aspect to consider is the size of the listening room and the distance from the speakers. Speaker specifications include sound pressure at a distance of 1 meter from the speaker with a 1W signal, typically expressed as a value such as 86 dB. Sound pressure decreases as the distance from the speaker increases, in proportion to the increase in the surface area of a sphere relative to its radius. This means that if the distance is doubled, the sound pressure decreases by 6 dB. For instance, at a distance of 2 meters, the corresponding speaker would output sound at 80 dB, and at a distance of 4 meters, it would be at 73 dB.

In a real enclosed room, the sound pressure decreases less due to the addition of reflections, and typically, an average reduction of 3 dB is considered when the distance is doubled. If you send a 10W signal instead of a 1W signal, the volume increases by 10 dB. Based on this, it appears that you don't really need a high amount of power. In the example provided, a speaker with fairly moderate sensitivity can produce sound at 10W, effectively filling the entire room at the recommended maximum sound level.

The second aspect to consider is how much of the speaker's rated power is usable. The power with minimal distortion from the speaker is usually around 20-50% of the maximum rated power. It can be assumed that there is a rule here: the less of the power is used, the fewer distortions there are. Unfortunately, this viewpoint is not entirely accurate. High power often leads to larger coils in the speakers, heavier diaphragms, and some other changes that aren't necessarily beneficial for accurate music reproduction. Without delving into details, if the usable power is 20 - 50% of the speaker's (loudspeaker's) maximum rated power, then the range is quite reasonable for high-quality music playback.

For home use, it's usually recommended to have 1-2 watts per square meter, depending on the desired volume level. Therefore, for a room of 10 square meters, a power of 10 - 20 watts per channel is necessary.

Taking into account the distortion-free ratio, it is safe to assume that 20W is needed per speaker, totaling 40 watts for pair. If you move to a room that's twice as large, then increase the power times two. This is not due to mathematics, but also because you might host different events in larger spaces, where the need for volume might be significantly higher compared to a cabinet or bedroom. Therefore, the initially suggested 400 W speaker pair is a suitable choice for filling an open space that spans multiple floors throughout the entire house.

The result is the realization that, when it comes to speakers, quality should be prioritized over quantity (power). In the same price range, a less powerful speaker with higher-quality components is a better choice than a more powerful one with inferior construction. In practical terms, all these speakers are already significantly more powerful than needed.

The same applies to amplifiers, but amplifier power costs little in terms of money, and there's no direct reason to save power here. A quarter more powerful amplifier than the speakers should suffice. If you want extra headroom, then go for a half more powerful amplifier.

Notes (which naturally exist in every acoustic and audio engineering topic):

Different aspects need to be distinguished when it comes to speaker power. The maximum allowed power is the loudspeaker's capacity to pass a signal without getting damaged. The continuous power rating depends on the loudspeaker's cooling and can be applied for prolonged periods. Distortion-free signal representation power is usually not included in specifications, but it's typically at least one-fifth to half of the maximum power. The sound quality remains optimal up to this level. We start with the maximum allowed power when considering relative figures, which the manufacturer often uses in the loudspeaker's designation or name. 

In terms of bass, attention should also be paid to the loudspeaker's size. A known saying provides guidance here: "There is no replacement for displacement." To some extent, bass can be added with a loudspeaker membrane that has longer excursion capabilities. Unfortunately, this linearly increases the volume of air moved while the area increases squared. So, a loudspeaker with a 20 cm diameter can move four times more air with the same excursion as a 10 cm diameter loudspeaker. There can be many exceptions, especially considering long excursion, multiple loudspeakers in series, etc. However, for a simple loudspeaker, a simpler rule can be taken: for a bedroom or an home office, a bass loudspeaker's diameter could start from 15 cm, and in a larger living room, either multiple smaller ones or starting from 20 cm. As an example, TiFi Elf bass loudspeakers have a nominal power of 80 W, 160 W for a pair. This seems sufficient for filling a fairly large room with sound, and based on power alone, it could cover up to 40 square meters. However, my room recommendation is still up to 20 square meters, mostly based on the bass loudspeaker's size, not the system's power.

The above discussion doesn't apply to near-field speakers. If the speaker is on your desk just a meter away, the size of the rest of the room is not significant. The same goes for creating a specific small listening area within a large room where the speakers are close to the listener.