Fig 2.17 The effect of noise exposure on hearing sensitivity
The ear is a sensitive and accurate organ of sound transduction and analysis. However, the ear can be damaged by exposure to excessive levels of sound or noise. This damage can manifest itself in two major forms:
Fig 2.18 Idealised form of the effect of noise on hearing bandwidth
This has two main effects: firstly, our ability to separate out; the different components of the sound is impaired, and this will reduce our ability to understand speech or separate out desired sound from competing noise. Interestingly it may well make musical sounds which were consonant more)) dissonant because of the presence of more than one frequency harmonic in a critical band. The second effect is a reduction in the heanng sensitivity, also shown in Flgure 2.18, because the enhancement mechanism also increases the amplitude sensitivity of the ear. This effect is more insidious because the effect is less easy to measure and perceive; it manifests itself as a difficulty in interpreting sounds rather than a mere reduction in their perceived level. Another related effect due to damage to the hair cells is noise induced tinnitus. Tinnitus is the name given to a condition in which the cochlea spontaneously generates noise, which can be tonal, random noises, or a mixture of the two. In noise-induced tinnitus exposure to loud noise triggers this, and as well as being disturbing, there is some evidence that people who suffer from this complaint may be more sensitive to noise induced hearing damage.
Fig 2.19 Audiograms of normal and damaged hearing
Because the damage is caused by excessive noise exposure it is more likely at the frequencies at which the acoustic level at the ear is enhanced. The ear is most sensitive at the first resonance of the ear canal, or about 4 kHz, and this is the frequency at which most hearing damage first shows up. Hearing damage in this region is usually referred to as an audiometric notch because of its distinctive shape on a hearing test, or audiogram, see Figure 2.19. This distinctive pattern is evidence that the hearing loss measured is due to noise exposure rather than some other condition, such as the inevitable high-frequency loss due to ageing.
How much noise exposure is acceptable? There is some evidence that the normal noise in Western society has some long-term effects because measurements on the hearing of other cultures have shown that there is a much lower threshold of hearing at a given age compared with Westerners. However, this may be due to other factors as well; for example, the level of pollution, etc. There is strong evidence, however, that exposure to noises with amplitudes of greater than 90 dB(SPL) will cause permanent hearing damage. This fact is recognised by legislation which requires that the noise exposure of workers be less than this limit. Note that if the work environment has a noise level of greater than this then hearing protection of a sufficient standard should be used to bring the noise level, at the ear, below this figure.
In many musical situations the noise level is greater than 90 dB(SPL) for short periods. For example the audience at a concert may well experience brief peaks above this, especially at particular instants in works such as Elgar's Dream of Gerontius, or Orff's Carmina Burana. Also in many practical industrial and social situations the noise level may be louder than 90 dB(SPL) for only part of the time.
Fig 2.20 Maximum exposure time as a function of sound level plotted on a linear scale (upper) and a logarithmic scale (lower)
How can we relate intermittent periods of noise exposure to continuous noise exposure for example,how damaging is a short exposure to a sound of 96 dB(SPL)? The answer is to use a similar technique to that used in assessing the effect of radiation exposure, that of 'integrated dose'. The integrated noise dose is defined as the equivalent level of the sound over a fixed period of time, which is currently 8 hours. In other words the noise exposure can be greater than 90 dB(SPL) providing that it is for an appropriately shorter time which results in a noise dose which is less than that which would result from being exposed to noise at 90 dB(SPL) for 8 hours. The measure used is the Leq mentioned earlier and the maximum dose is 90 dB Leq over eight hours. This means that one can be exposed to 93 dB(SPL) for 4 hours, 96 dB(SPL) for 2 hours, and so on. Figure 2.20 shows how the time of exposure varies with the sound level on linear and logarithmic time scales. It can be seen that exposure to extreme sound levels, greater than 100 dB(SPL), can only be tolerated for a very short period of time, less than half an hour. There is also a limit to how far this concept can be taken because very loud sounds can rupture the eardrum causing instant, and sometimes permanent, loss of hearing.
This approach to measuring the noise dose takes no account of the spectrum of the sound which is causing the noise exposure, because to do so would be difficult in practice. However, it is obvious that the effect of a pure tone at 90 dB(SPL) on the ear is going to be different to the same level spread over the full frequency range. In the former situation there will be a large amount of energy concentrated at a particular point on the basilar membrane and this is likely to be more damaging than the second case in which the energy will be spread out over the full length of the membrane. The specification for noise dose uses' A' weighting for the measurement which, although it is more appropriate for low rather than high sound levels, weights the sensitive 4 kHz region more strongly.
Hearing loss is insidious and permanent and by the time it is measurable it is too late. Therefore in order to protect hearing sensitivity and acuity one must be proactive. The first strategy is to avoid exposure to excess noises. Although 90 dB(SPL) is taken as a damage threshold if the noise exposure causes ringing in the ears, especially if the ringing lasts longer than the length of exposure, it may be that damage may be occurring even if the sound level is less than 90 dB(SPL). There are a few situations where potential damage is more likely.
In both cases the levels are under your control and so can be reduced. However, there is an effect called the acoustic reflex (see Section 2.1.2), which reduces the sensitivity of your hearing when loud sounds occur. This effect, combined with the effects of temporary threshold shifts, can result in a sound level increase spiral, where there is a tendency to increase the sound level 'to hear it better' which results in further dulling, etc. The only real solution is to avoid the loud sounds in the first place. However, if this situation does occur then a rest away from the excessive noise will allow some sensitivity to return.
There are sound sources over which one has no control, such as bands, discos, night clubs, and power tools. In these situations it is a good idea either to limit the noise dose or, better still, use some hearing protection. For example, one can keep a reasonable distance away from the speakers at a concert or disco. It takes a few days, or even weeks in the case of hearing acuity, to recover from a large noise dose so one should avoid going to a loud concert, or night club, every day of the week! The authors regularly use small 'in-ear' hearing protectors when they know they are going to be exposed to high sound levels, and many professional sound engineers also do the same. These have the advantage of being unobtrusive and reduce the sound level by a modest, but useful, amount (15-20 dB) while still allowing conversation to take place at the speech levels required to compete with the noise! These devices are also available with a 'flat' attenuation characteristic with frequency and so do not alter the sound balance too much, and cost less than a CD recording. For very loud sounds, such as power tools, then a more extreme form of hearing protection may be required, such as headphone style ear defenders.
Your hearing is essential, and irreplaceable, for both the enjoyment of music, for communicating, and socialising with other people. Now and in the future, it is worth taking care of.
How do we perceive the direction that a sound arrives from? The answer is that we use our two ears but how?
Fig 2.21 The effect of the direction of a sound source with respect to the head
Because our two ears are separated by our head, this has an acoustic effect which is a function of the direction of the sound. There are two effects of the separation of our ears on the sound wave: firstly the sounds arrive at different times and secondly they have different intensities. These two effects are quite different so let us consider them in turn.
Consider the model of the head, shown in Figure 2.21, which shows the ears relative to different sound directions in the horizontal plane. Because the ears are separated by about 18 cm there will be a time difference between the sound arriving at the ear nearest the source and the one further away. So when the sound is off to the left the left ear will receive the sound and when it is off to the right the right ear will hear it first. If the sound is directly in front, or behind, or anywhere on the median plane, the sound will arrive at both ears simultaneously. The time difference between the two ears will depend on the difference in the lengths that the two sounds have to travel. A simplistic view might just allow for the fact that the ears are separated by a distance d and calculate the effect of angle on the relative time difference by considering the extra length introduced purely due to the angle of incidence, as shown below.
Fig 2.22 A simple model for the time difference
This assumption will give the following equation for the time difference due to sound angle:
Δt = d sin(θ)/c
Δt = the time difference between the ears (in 5)
d = the distance between the ears (in m)
θ= the angle of arrival of the sound from the median (in radians)
and c = the speed of sound (in ms-1)
Unfortunately this equation is wrong. 11: underestimates the delay between the ears because it ignores the fact that the sound must travel around the head in order to get to them. This adds an additional delay to the sound, as shown in Figure above. This additional delay can be calculated, providing one assumes that the head is spherical, by recognising that the distance travelled around the head for a given angle of incidence is give by:
Δd = r x θ
Δd = the extra path round the head at a given angle of incidence (in m) and r = half the distance between the ears (in m). This equation can be used in conjunction with the extra pathlength due to the angle of incidence, which is now a function of r, as shown in Figure 2.24, to give a more accurate equation for the ITD as:
ITD = r ( θ + sin(θ))/c
Fig 2.23 The effect of the pathlength around the head on the interaural time difference
Fig 2.24 A better model
Use this equation to find the maximum IDT which occurs at 90 degrees (PI/2 radians) to be:
IDT max = (0.09 m X (pi/2 + sin(pi/2)/344 m/s) = 6.73 X 10^-4 s = 673 microseconds
Fig 2.25 The interaural ITD as a function of angle
This is a very small delay but a variation from this to zero determines the direction of sound, at low frequencies. Figure above shows how this delay varies as a function of angle, where positive delay corresponds to a source at the right of the median plane and negative delay corresponds to a source on the left. Note that there is no difference in the delay between front and back position, at the same angle. This mean' that we must use different mechanisms and strategies to differentiate between front and back sound,. There is also a frequency limit to the way in which sound direction can be resolved by the ear in this way. This is due to the fact that the ear appears to use the phase shift in the wave caused by the interaural time difference to resolve the direction. That is the ear mesures the phase shift given by:
<I>ITD = 2PIfr(theta + sine(theta))
where <I>ITD = the phase difference between the ears (in radians)
and f = the frequency (in Hz)
When this phase shift is greater than PI radians (180°) tlme will be an unresolvable ambiguity in the direction because there are two possible angles-one to the left and one to the right-that
could cause such a phase shift. This sets a maximum frequency, at a particular angle, for this method of sound locatiation, which is given by
fmax(theta) = 1/(2 X 0.09 X (theta + sin(theta))
which for an angle of 90° is:
fmax (0 = n/2) = 2 x 0.09 m x (n/2 + sin(n/2» = 743 Hz
Thus for sounds at 90° the maximum frequency that can have its direction determined by phase is 743 Hz. However, the ambiguous frequency limit would be higher at smaller angles.
The other cue that is used to detect the direction of the sound is the differing levels of intensity that result at each ear due to the shading effect of the head. This effect is shown in Figure 2.26 which shows that the levels at each ear is equal when the sound source is on the median plane but that the level at one ear progressively reduces, and increases at the other, as the source moves away from the median plane. The level reduces in the ear that is furthest away from the source. The effect of the shading of the head is harder to calculate but experiments seem to indicate that as the intensity ratio between the two ears varies sinusoidally from 0 dB up to 20 dB, depending on frequency, with the sound direction angle, as shown in Figure 2.27. However, as we saw in Chapter 1, an object is not significant as
Fig 2.26 The effect of the head on the interaural intensity difference
Fig 2.27 The IDT as a function of angle and frequency
a scatterer or shader of sound until its size is about two thirds of a wavelength (%1..), although it will be starting to scatter an octave below that frequency. This means that there will be a minimum frequency below which the effect of intensity is less useful for localisation which will correspond to when the head is about one third of a wavelength in size (~A.). For a head the diameter of which is 18 cm, this corresponds to a minimum frequency of:
fmin(theta=PI/2) = 1/3 (c/d) = 1/3 x (344/0.18m) = 637 Hz
Thus the interaural intensity difference is a cue for direction at high frequencies whereas the interaural time difference is a cue for direction at low frequencies. Note that the cross-over between the two techniques starts at about 700 Hz and would be complete at about four times this frequency at 2.8 kHz. In between these two frequencies the ability of our ears to resolve direction is not as good as at other frequencies.
The above models of directional hearing do not explain how we can resolve front to back ambiguities or the elevation of the source. There are in fact two ways which are used by the human being to perform these tasks.
The first is to use the effect of our ears on the sounds we receive to resolve the angle and direction of the sound. This is due to the fact that sounds striking the pinnae are reflected into the ear canal by the complex set of ridges that exist on the ear. These pinnae reflections will be delayed, by a very small but signifi cant amount, and so will form comb filter interference effects on the sound the ear receives. The delay that a sound wave experi ences will be a function of its direction of arrival, in all three dimensions, and we can use these cues to help resolve the ambiguities in direction that are not resolved by the main directional hearing mechanism. The delays are very small and so these effects occur at high audio frequencies, typically above 5 kHz. The effect is also person specific, as we all have differently shaped ears and learn these cues as we grow up. Thus we get confused for a while when we change our acoustic head shape radically, by cutting very long hair short for example. We also find that if we hear sound recorded through other people's ears that we have a poorer ability to localise the sound, because the interference patterns are not the same as those for our ears.
The second, and powerful, means of resolving directional ambiguities is to move our heads. When we hear a sound that we wish to attend to, or resolve its direction, we move our head towards the sound and may even attempt to place it in front of us in the normal direction, where all the delays and intensities will be the same. The act of moving our head will change the direction of the sound arrival and this change of direction will depend on the sound source position relative to us. Thus a sound from the rear will move in different direction compared to a sound in front of or above the listener. This movement cue is one of the reasons that we perceive the sound from headphones as being 'in the head'. Because the sound source tracks our head movement it cannot be outside and hence must be in the head. There is also an effect due to the fact that the headphones also do not model the effect of the head. Experiments with headphone listening which correctly model the head and keep the source direction constant as the head moves give a much more convincing illusion.
Because both intensity and delay cues are used for the perception of sound source direction one might expect the mechanisms to be in similar areas of the brain and linked together. If this were the case one might also reasonably expect that there was some overlap in the way the cues were interpreted such that intensity might be confused with delay and vice versa in the brain. This allows for the possibility that the effect of one cue, for example delay, could be cancelled out by the other, for example intensity. This effect does in fact happen and is known
Fig 2.28 Delay versus intensity trading
as interaural time difference versus interaural intensity difference trading. In effect, within limits, an interaural time delay can be compensated for by an appropriate interaural intensity difference, as shown in Figure 2.28, which has several interesting features. Firstly, as expected time delay versus intensity trading is only effective over the range of delay times which correspond to the maximum interaural time delay of 673 microseconds, beyond this amount of delay small intensity differences will not alter the perceived direction of the image. Instead the sound will appear to come from the source which arrives first. This effect occurs between 673 miocroseconds and 30 ms. However, if the delayed sound's amplitude is more than 12 dB greater than the first arrival then we will perceive the direction of the sound to be towards the delayed sound. After 30 ms the delayed signal is perceived as an echo and so the listener will be able to differentiate between the delayed and undelayed sound. The implication of these results are two-fold; firstly, it should be possible to provide directional information purely through either only delay cues or only intensity cues. Secondly, once a sound is delayed by greater than about 700 microseconds the ear attends to the sound that arrives first almost irrespective of their relative levels, although clearly if the earlier arriving sound is significantly lower in amplitude, compared to the delayed sound, then the effect will disappear.
The second of the ITD and lID trading effects is also known as the Haas, or precedence, effect, named after the experimenter who quantified this behaviour of our ears. The effect can be summarised as follows:
These results have important implications for studios, concert halls and sound reinforcement systems. In essence it is important to ensure that the first reflections arrive at the audience earlier than 30 ms to avoid them being perceived as echoes. In fact it seems that our preference is for a delay gap of less than 20 ms if the sound of the hall is to be classed as 'intimate'. In sound reinforcement systems the output of the speakers will often be delayed with respect to their acoustic sound but, because of this effect, we perceive the sound as coming from the acoustic source, unless the level of sound from the speakers is very high.
Because of the way we perceive directional sound it is possible to fool the ear into perceiving a directional sound through just two loudspeakers or a pair of headphones in stereo listening. This can be achieved in basically three ways, two using loudspeakers and one using headphones. The first two ways are based on the concept of providing only one of the two major directional cues in the hearing system. That is using either intensity or delay cues and relying on the effect of the ear's time-intensity trading mechanisms to fill in the gaps. The two systems are as follows:
Fig 2.29 Delay stereo recording
change in performer position does not alter the delay between the two sounds. However, because the microphones are directional the intensity received by the two microphones does vary. So the two channels when presented over loudspeakers contain predominantly directional cues based on intensity to the listener. Intensity stereo is the method that is mostly used in pop music production as the pan-pots on
Fig 2.30 Intensity Stereo recording
a mixing desk, which determine the position of a track in the stereo image, vary the relative intensities of the two channels, as shown below.
Fig 2.31 The effect of the pan pots in a mixing desk on the intensity of the two channels
These two methods differ primarily in the method used to record the original performance and are independent of the listening arrangement, so which method is used is determined by the producer or engineer on the recording. It is also possible to mix the two cues by using different types of microphone arrange ment-for example slightly spaced directional microphones and these can give stereo based on both cues. Unfortunately they also provide spurious cues, which confuse the ear, and getting the balance between the spurious and wanted cues, and so providing a good directional illusion is difficult.
The main compromise in stereo sound reproduction is the presence of spurious direction cues in the listening environment because the loudspeakers and environment will all contribute cues about their position in the room, which have nothing to do with the original recording.
Before next class please read Sections
pages 109 to 119 of Acoustics and Psychoacoustics. We may have a brief quiz on these sections at the beginning of the next class.