Measuring and perceiving loudness: Pascals, decibels and phons

Hearing and listening is a complicated mix of physical detection, coding and subjective perception. We need to understand about sound and sound measurement in order to be able to control the physical stimulus, for sound production, hearing aids, telephony and many other purposes.

Sound can be measured, but sounds of different energy strength are perceived as having different loudness, and whilst there are published average data on the relationship, loudness is individually perceived. To make it that bit more complicated, the human ear is more sensitive to some frequencies than others. Loudness is a subjective judgment of the energy level of the sound. As sound results from vibrations in the air, otherwise thought of as pressure changes, it makes sense to measure sound in sound pressure level. When we do this, the absolute measure is in Pascals.

Measuring sound in a way that makes sense to talk about has resulted in the use of the decibel, which is a ratio of two physical measurements. This is sensible because the ear can detect sound over such an extra-ordinarily wide range of sound pressures. The sound pressure of a sound that we would find painfully loud is about a million times greater than the softest sound we can hear; 20 million µPa vs 20µPa. This doesn’t make a very convenient way to measure sound – the softest sound is not zero, and sounds of more volume have lot of “zeros” to contend with. And so,  the decibel scale – a ratio scale – was invented, where the softest sound that an average group of volunteers could hear was established as 0 dB SPL (Sound Pressure Level). Getting to the decibel from a measure of pressure wasn’t entirely straight forward. Our ears respond to pressure changes, so we have a measurement system that relates to the measurement of pressure, but it was devised in a roundabout way. Initially, sound measurements can be made as units of energy, or intensity. Sound intensity which causes pain is a billion times greater than that of the softest sound you can hear. The sound pressure level of a sound is:

Sound level = 20 log (pmeasured/preference) = 20 log 1 = 0 dB

Doubling the sound pressure level gives an increase of 6dB. If the sound pressure is ten times as much, the sound pressure level is +20dB.

So where does loudness come into this? Loudness is a subjective feeling and is not measured in decibels. We don’t judge sounds of the same sound pressure level, but at different frequencies to be equally loud. The unit of loudness is the phon. There is a standard definition for the phon: One phon is equal to One dB SPL at a frequency of one kHz.  . To find out how we hear at different frequencies, scientists have worked with a large group of young people, described as otologically (ear health) normal, and asked them to match the loudness of sounds at different pitches (pure tone stimuli). This has led to a map of equal loudness contours.

Having just absorbed that doubling the sound pressure increases the sound level by 6dB, now take on board that a doubling of loudness is about an increase of 10dB. However, the perceived loudness of the sound depends on several different factors: the amplitude, the sound pressure level, the frequency, and the time behaviour of the sound. There’s more though. Loudness even depends on simultaneous other sensory experiences. So “loudness” and “volume” can’t be measured by instruments: they are subjective.

noisy fort

So, let’s summarize:

When we are measuring sound, pressure changes are recorded and expressed as decibels

  • The dB scale is a ratio scale
  • Doubling the sound pressure, results in an increase of 6dB
  • Doubling the loudness results in an increase of about 10dB.

Loudness perception is also affected by the duration and the “bandwidth” of the sound.   Bandwidth is a topic for another day, but think of the bandwidth as involving more detectors in the inner ear. Generally speaking, and it is of course a bit more complicated than this, if more detectors are involved, then a sound is perceived as louder. There is a limit to their involvement, which is why it is only a 10dB increase for a doubling of loudness.

People with normal hearing are most sensitive to sounds around 2–4 kHz, and less sensitive either side of this zone. Children can hear up to about 20 kHz, although they are much less sensitive to the very high frequencies than around the 2-4kHz. Sensitivity to high frequencies deteriorates over our life for most people. By the age of fifty five, perception of sounds above 4kHz is commonly much reduced, and by 65 sounds above 2kHz need much higher input. Sadly, these sounds that need increased levels to hear are also important for hearing speech sounds.

A simple understanding of the relationship between sound measurement and loudness perception starts to make it clear why trying to set up hearing aids to a physical sound pressure prediction, based on averaged data, is a counter intuitive path, which necessitates lots of measurements that can be bypassed by going to the chief controller – the brain.

This is one of the reasons that the Blamey Saunders way of setting up hearing aids is the best, because it is based on your judgement of loudness. We don’t do things the old fashioned way — we do things based on contemporary research.

And remember –

“One person’s data is another person’s noise.” ― K.C. Cole

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  1. Turns out, the maxium possible sound level in air is 194 dB.
    That’s because sound is a wave, oscillating from high to low pressure. On the high side of the wave, it can get to 1 over normal atmosphere pressure, but on the low side, you can’t have less than zero atmosphere pressure.
    The bottom of the wave sort of bumps into the floor at zero atmospheres. This occurs at about 194 dB.
    I’m not entirely clear what happens with something super-loud such as an atomic blast. The top of the wave would go way over this limit, but the bottom part of the wave has nowhere to go.

    Rod Taylor
    1. There is sound measurement and sound perception, so the point about explosions, which damage the ear, is good.
      If a tree falls in a forest and there is no one there to hear it is there a sound?

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