Click here to purchase the entire book in PDF format. Threshold of Hearing In the previous chapter, we said that the threshold of hearing at 1 kHz is 20 $\mu$Pa or 0 dBspl. If a sine tone is quieter than this, you will not hear it. If you tried to find the threshold of hearing for a frequency lower than 1 kHz, you would find that it's higher than 20 $\mu$Pa. In other words, in order to hear a tone at 100 Hz, it will have to be louder than 0 dBspl - in fact, it will be about 25 dBspl. So, in order for a 100 Hz tone to sound the same level as a 1 kHz tone, the 100 Hz tone will have to be higher in measurable level. Take a look at the red curve in Figure 5.8. This line shows you the threshold of hearing for different frequencies. There are a couple of important characteristics to notice here. Firstly, notice that frequencies higher lower than 1 kHz and higher than about 5 kHz must be higher than 0 dBspl in order to be audible. Secondly, for frequencies lower than 100 kHz, the lower in frequency, the higher the threshold. Thirdly, for frequencies higher than 5 kHz, the higher the frequency the higher the threshold. Finally, notice that there is a dip in the threshold of hearing between 2 kHz and 5 kHz. This means that you are able to hear frequencies in this range even if they are lower than 0 dBspl. This frequency band in which our hearing is most sensitive is an interesting area for two reasons. Firstly, the bulk of our speech (specifically consonant sounds) relies on information in this frequency range (although it's like that the speech evolved to capitalize on the sensitive frequency range). Secondly, the anthropologically-minded will be interested to note that the sound of a snapping twig has lots of information which is smack in the middle of the 2 kHz - 5 kHz range. This is a useful characteristic when you look like lunch to a large-toothed animal that's sneaking up behind you... Figure 5.8: Equal loudness contours [Zwicker and Fastl, 1999]. The red curve at the bottom is the threshold of hearing. One interesting thing to note here is that points along the red curve in this graph all indicate the threshold of hearing, meaning that two sinusoidal tones with sound pressure level indicated by the curve will appear to us to be the same level, even though they aren't in reality. For example, looking at Figure 5.8, we can see that a tone at 50 Hz and a sound pressure level of 40 dBspl will be on the threshold of hearing, as will a 1 kHz tone at 0 dBspl and a 10 kHz tone at about 5 dBspl. These three tones at these levels will have the same perceived level - they will appear to have equal loudness. The point that I'm making here is that, if you change the frequency of a sinusoidal tone, you'll have to change the sound pressure level to keep the perceived level the same. This is true even if you're not at the threshold of hearing. Take a look at the remaining curves in Figure 5.8. For example, look at the curve that intersects 1 kHz at 20 dBspl. You'll see that this curve also intersects 100 Hz at about 38 dBspl. This indicates that, in order for a 1 kHz tone at 20 dBspl to sound the same perceived loudness as a 100 Hz tone, the lower frequency will have to be about 38 dBspl. Consequently, the curve that we're looking at is called an equal loudness contour - it tells us what the actual levels of multiple tones have to be in order to have the same apparent level. These curves were first documented in 1933, by a couple of researchers by the name of Fletcher and Munson [Fletcher and Munson, 1933]. Consequently, the equal loudness contours are sometimes called the Fletcher and Munson Curves. Notice that the curves tend to flatten out when the level goes up. What does this mean? Firstly, when you turn down your stereo, you are less sensitive to low and high frequencies (compared to the mid-range frequencies) than when the stereo was turned up. Therefore the timbral balance changes, particularly in the low end. If the level is low, then you'll think that you hear less bass. This is why there's a loudness switch on your stereo. It boosts the bass to compensate for your low-level equal loudness curves. Secondly, things simply sound better when they're louder. This is because there's a ``better balance'' in your hearing perception than when they're at a lower level. This is why the salesperson at the stereo store will crank up the volume when you're buying speakers... they sound good that way because a higher level means you hear more bass.