Therefore the formula shows that the time difference will be 1 ÷ 1130 which is 0.889 milliseconds or approximately 0.9 ms. This number will be useful later as it is also the time taken for sound to travel one foot, so when multiplied by the path difference in feet it gives the delay time. The reason for using feet per second in this report rather than the standard SI units of meters per second is that due to the human ears being very close to 1 foot apart it makes all of the calculations far more simple and seeing as what is required is simply the time delay, the unit of distance is not important as they both give answers in seconds.
Therefore 0.9 milliseconds later the left ear starts to pick up the sound. This sound get processed too and goes to the brain, where without thinking about it the human brain automatically measure the time delay between the sound from right and left ears. In this case the sound has taken the longest possible time difference between the two ears, because the sound was directly to the side. However, had the sound come from the left, the time delay would have been of the same magnitude but in the opposite direction, because the right ear would have heard the sound last rather than before the left ear. Also, if the sound was either directly in front or directly behind, the time delay between the two sounds would have been zero. Therefore as a sound travels around the head in a circle, the delays, gradually get longer and then shorter and then reverse in a sine wave like pattern. This wave is relevant because you can use the sine wave along with trigonometry to actually calculate the angle at which the sound must have come from originally, and this is exactly what your brain is doing all the time.
From a very early age, the human brain learns the maximum time delay between its ears and adjusts the senses to that limit. As the head grows with age, sound location does not suffer, therefore the human brain must be capable of adjusting these limits over time.
This simple phenomenon uses basic mathematical instinct to find sound direction. As it was stated earlier, all that is required is some simple trigonometry. The human brain knows the distance between its ears and the time delay between hearing each sound and thus the path difference of the sound to each ear. A simple drawing below will help to explain how the angle of the source of the sound can be established using trigonometry.
From the drawing you can see that the length of two sides are known in a right angled triangle, therefore you can use trigonometry. The 7 inch side can be calculated using the following formula:
time delay x 1130 ft/s
In this case the adjacent side and the hypotenuse are known so the following equation can be used where Θ stands for the angle from the right hand side to the source (THETA).
cos Θ = 7 ÷ 12
Θ = cos-1 (7 ÷ 12)
Θ = 54.31°
From this simple use of mathematics the direction of the sound was quickly found. However it is important to realize that the human brain is naturally doing this calculation hundreds of times a minute. However it does not do the calculation in the same calculator method as it was just done, the brain simply remembers what different time delays stand for, which is why it can adapt so easily. It has a feel for the different values in a primitive lookup table which explains why a person instantly knows where a sound came from, they do not hear it and then work out where from.
Experiments into shared source pulses arriving with delay.
Looking back at the original three sections of the Haas effect it can be seen that the second observation can have some interesting effects when exploited in a few simple experiments. This second effect observed is related to how the human brain can choose to ignore sounds which it knows are useless and confusing to speech recognition. The most obvious example of this is removing very close echoes from a voice or sound to make it easier to understand and pinpoint its location. This effect ties in with the previous observation because it relies entirely on the time delay between sounds and how the brain can track all the different sounds at once to sense echoes and cancel them out before it tries deciphering what was said or heard.
A small experiment which can be carried out to help explain this phenomenon requires a musical metronome and a tapping stick (drumstick or even a pencil) If the metronome is set ticking away somebody tries tapping the pencil in time with the beat of the metronome they will normally tap slightly ahead of the click creating an obvious noise of the two together. This is a normal thing to happen and will go on for a while until every now and then a very loud metronome click will be observed with no accompanying pencil tap at all and sometimes there will be a very loud pencil tap with no metronome beat. This is a prime example of the Haas Effect in which echoes are singled out to enhance the original sound. This can be explained by realising that once a musical object is struck it goes into a characteristic form of chaos for a little while until it settles down into its standard vibration pattern which created the sound we are familiar with. The human brain has evolved to listen out for this chaotic attack (or transient) as it represents the beginning of a new sound out of the mumble of other noises taking place in the background. It seams that the human brain is constantly on the lookout for these tell tail transitions and it is quite a complicated process to distinguish between separate sounds which happen very close together. The area of the brain looking out for these transitions between chaotic vibration and ordered sound seams unable to distinguish between separate sounds if they both arrive within 35 ms of each other. If the sounds do arrive within this time gap the human brain merges the two sounds together into one with approximately twice the amplitude. This explains the results of the experiment carried out above as the brain could not distinguish between the pencil tap and metronome tick so it automatically merged the two together to create one sound. As it happens with short sounds the brain can distinguish more easily and therefore the two beats were closer to 20 ms apart. Therefore the Haas effect explains that the two sounds were replaced by the single sound which arrived slightly earlier. It is easy to see that this effect could be useful as you can fool the brain into hearing things more loudly and hiding unwanted sounds which happen shortly after.
Modern music is often compressed into a digital format known as an MP3. The main function of this format is to save digital storage space so that many audio tracks can be stored in a cheaper memory space. One method of compressing the audio actually uses the Haas effect. An MP3 can by encoded as a constant bit rate which stands for the number of bit of data for 1 second of audio. However the newer MP3s can be encoded as a variable bit rate which means that when not much is happening in the track (e.g. silence) the bit rate drops momentarily to save storage space. A new method involves dropping the bit rate for 20 ms after a sharp beat in the music because it is known that the brain will ignore the quality of the sounds produced after this beat and mask them with the sound of the beat with the added volume of the following noise. All of this helps in the aim of reducing file size but is also a nice example of a practical use of the Haas effect.
For normal audio if a repeat sound is heard within 25-35 ms a person will not hear it even if the echo is up to 10bD louder than the source. This is an example of human sensory inhibition which applies to all our senses. The graph below help to show the effects experienced for different time gaps. The strong peak between 1 and 30 ms shows where the Haas effect has the biggest presence.
The brain will listen to the first sound with both ears and distinguish where it came from by using the trigonometric ideas shows above. Once it has the physical position of the source it will then block out any echoes received within the Haas time window. These echoes (which may be louder as stated above) are all merged into one sound with the same position and feel as the original sound. Therefore the brain can take the position from the first sound and the volume from the second. This effect is outstanding as it overcome the problem of sitting next to a loudspeaker at the back of a hall with an opera singer at the front. If this were the case the singer will be singing into the audience as well as a microphone. For people at the front this is no problem as they are probably sat closer to the singer than the speakers, so the brain will block out the loudspeakers but in the case below there is a larger problem.
It can be seen from the diagram above, that the person in the back of the audience has a speaker 6ft away and the original singer 73ft away. Sound travels at a very slow speed compared to the signal from the microphone to the loudspeaker (speed of light = 984,300,000 ft/sec) Light travels so quickly compared to sound that we can ignore its finite speed and assume it arrives instantly. Therefore by using the speed distance time equation shown before we know that sound takes 0.889 ms to travel one foot therefore you can calculate the time delay between the person hearing each sound.
A: 73 x 0.889 = 65 ms
B: 6 x 0.889 = 5 ms
Therefore the sound from the loudspeaker will arrive 60 ms earlier than the sound from the singer. This gap is larger than the 35 ms Haas cut off therefore the singer will be heard and then a much louder echo (from the close speaker) will arrive making the singing sound terrible and extremely difficult to understand. To remove the echo from the listener a delay could be set up of 60 ms in the electrical circuit in the sound system. This would now mean both sounds would arrive at the same time for the listener in the back row. The brain would pick the sounds up and you would hear a more coherent sound coming from both locations. However, the Haas effect can now be used by adding an extra delay of 15 ms to the digital delay circuit.
The diagram above shows, firstly a simple audio circuit with an amplifier and loudspeaker. The second shows how the digital delay unit should be put into the system to get the desired effect. An example of a digital delay unit used specifically for the Haas effect is Outboard Electronics’ TiMAX
Therefore for the back row the singer’s voice will be hear first, followed by the much louder sound from the close speaker, however the brain will block out this sound assuming it to be an echo and create a single, very loud, coherent sound coming from the speaker. Even if the person listens for the speaker, they will be convinced it is switched off. All they will here coming from the speaker is the noise and distortion picked up on the way. The people sitting in the rows closer to the front will have an even longer delay for the back speaker and thus it should still fall into the Haas window for them as well. Therefore everybody in the hall hears a perfect and loud sound, without being biased by sitting near speakers. If the hall is too large so that the time delay back to the front would cause another echo from the rear speaker for front row listeners then the Kutreff Effect can be used by adding extra speakers in the space between with smaller delays.
From the research Haas carried out it appeared that for pulselike signals an autocorrelation function for coherence could be formulated for different values of delay τ there is a formula to estimate the coherence. The formula is taken from the Bipolar Transmission Line Project website:
The meaning of the above formula is as follows.
f( t ) is the function of the initial sound.
f( t-τ ) is the function of the delayed sound where τ is the delay.
R(τ) is a function of the delay which can be used to measure the coherence in different sounds observed by the listener. The formula states that the integral of the two sound functions multiplied together between limits of plus and minus infinity.
When this function is plotted for different values of delay in ms ranging from 0 – 5 ms you get a curve starting from 1 and dropping quickly at first and then more shallowly to reach a steady value of around 0.2 The graph is included below.
This covers all of the effects which Haas discovered and has also included many of their different uses in modern society, the basics of human hearing using the physical method of trigonometry and distance time calculations naturally are now understood and a lot more has been learnt about just how much physics the brain is calculating constantly throughout the day.
Evaluation:
From the research which was carried out on this project a great deal was learnt about the different discoveries which Haas made. However some of the different sources were slightly contradictory as to the exact values of the Haas Window. The more simplistic sources like Charles Macchia’s paper seamed to make far more sense as to the different values as it gave more examples which could be followed explaining where each number was to be used. For example there is no consistency as to the Haas cut off point, some sources quote it as 35 ms, some as 25 ms. the information used to draw the graph of the area in which the effect works best also seams to go up much higher than the 35 ms cut off point.
Bibliography
These findings are taken from the translation of Haas’s original paper on the Haas effect.
Haas Quantising Effect by Charles Macchia explains these ideas of how the chaotic sounds are picked out from the background. This source is very useful as it gives a different viewpoint on the more complex Haas effect. The timing values used here are not linked with the values of the Haas Window. Charles explains how the values are much smaller for punchy sounds like a pencil tap than they are for constant music or speech. However these ideas do give a good introduction into the basic effects which Haas discovered and wrote about in his paper on the subject.
Values for drawing graph from soundinstitute.com to highlight the area in which the Haas effect is most relevant.
Outboard electronics’ website explains that “The Kutruff Effect further demonstrates that the upper limit of delay can be extended from Haas's maximum of 30mS by adding more loudspeakers with additional delays, so for example in a three loudspeaker system provided both the delay from speaker 1 to speaker 2 and the delay to speaker 2 to speaker 3 are within the Haas range, the image can be pulled from speaker 3 to speaker 2 to speaker 1 , even though the total delay from the speaker 1 to 3 exceeds the Haas maximum…”
