Physics Of Hearing I PDF

Physics of Hearing I The type of wave perceived in the process of hearing is a pressure wave ○ In the eye = EM wave ○ In the ear = Pressure wave Pressure waves are present everywhere as the air is full of molecules that can be excited. They’ll be perceived by the presence of 3 specific parts in our...

Physics of Hearing I The type of wave perceived in the process of hearing is a pressure wave ○ In the eye = EM wave ○ In the ear = Pressure wave Pressure waves are present everywhere as the air is full of molecules that can be excited. They’ll be perceived by the presence of 3 specific parts in our ear: outer, middle and inner ear. Each of these parts has a different role, a reason for being where they are. The most important part, from our point of view, occurs in the inner ear. The incoming pressure waves will trigger an electrical impulse in the nerves. - The outer ear is not very relevant, it only conveys the wave to the eardrum, an elastic membrane. This membrane will respond to the stimulation of the pressure wave, as it makes it oscillate around its equilibrium position. - Next, there are 3 ossicles within the middle ear in which there are joints. They’re found connecting the eardrum with the oval window. Through these ossicles, the vibration of the eardrum is transported from the external eardrum to a “window” in the cochlea, the oval window. - This oval window connects the middle with the inner ear. This cavity, the cochlea, is filled with a fluid which is mainly water. We will need to transport an oscillation from air, and transfer it to water. Once injected in the liquid, the oscillation will be able to trigger an electrical impulse from the basilar membrane. Why is this specific mechanism necessary in order to perform this transfer from outer to inner ear? MECHANISM OF HEARING Drawing: outer ear, membrane (eardrum), 3 ossicles connected to another membrane which is placed within the oval window, at the beginning of the cochlea. In the drawing, the cochlea is not represented as spiral. The cochlea is a spiral channel, which actually contains 2 different internal channels (upper and lower), that are connected at the top. Once it crosses the oval window, the oscillation ascends along the spiral cochlea and then passes through the connection to the other channel, descending towards the round window. It’s in this location, along the basilar membrane, which divides the cochlea into 2 channels, where the nerve impulse will be generated. In order to understand the mechanisms necessary in order for the pressure wave to reach this cochlea, let’s propose a situation. What would happen if instead of this system, we have a simpler situation (NOT real)? Incoming pressure wave from air→ membrane→ water (this is NOT the real situation). In this configuration, we would need to transfer the wave directly to water. However, the property of acoustic impedance (density of water is roughly 1000x the density of air) makes it impossible for the majority of the pressure wave to be transmitted into the water. The P wave in the water will be imperceptible. WE NEED SOMETHING THAT AMPLIFIES THE PRESSURE WAVE, so when it’s diminished as it passes into water, it will still be able to be perceived by the nerves. 1. 1st amplification factor = because of the ratio between the area of the eardrum and oval window. The Area of the eardrum is roughly 20 times the area of the oval window (Ae = 20 Aow). The energy that arrives at the eardrum is transported to a much smaller area, and this fact produces a great amplification of the pressure wave as it contacts the membrane to pass into the water. The intensity is increased 2. 2nd amplification factor = the ossicles are levers. We have 3 different ones, which connect the eardrum with the oval window. They produce a supplementary amplification. When we combine these 2 factors, we get a factor of amplification that compensates the injection in water (which diminishes the pressure wave due to acoustic impedance) Problems can arise in these amplification mechanisms: - Hole in the membrane = decrease in the amplification factor. The threshold to trigger an impulse in the inner ear will be increased. These people will need a louder sound to induce the same response from the nerves. - Problems in the ossicles will also reduce the amplification factor This is the whole reason for why we need the middle ear to perceive sounds. CHARACTERISTICS OF SOUND Sound is characterized mainly by 3 things: Pitch. Can be defined as the frequency of the incoming sound waves Intensity. Defined as how much energy arrives per square metre per second. How do we perceive this intensity? We’ll see it in a moment. But we know its perception is in the logarithmic scale “Timbre” (next session) Pitch level of the sound wave For the same intensities, the pitch can be very different. As you get older, your threshold increases. You can’t hear as many sounds. 1st point: the perception of sound changes a lot depending on the person. There are many more variations than in visual perception. The pitch perception is very different depending on the person. Audible sound waves are pressure waves between 20Hz-20KHz. This is the normal range of frequencies. - Below 20 Hz, they are infrasound - Over 20KHz, they are ultrasounds and we cannot perceive them. This definition of sound is only valid for young people. For young ears, whose threshold of sound still remains within this normal range of values. Intensity of the sound wave The intensity of sound, on the other hand, is something quite peculiar. Perception is different from the physical stimulus. The physical stimulus, we can measure with a specific device, while the perception is what happens in the brain when we process an incoming stimulus. The point we must highlight is that this property is particularly important when referring to sound. The human brain is able to perceive local changes of physical magnitudes. It can’t perceive the physical stimulus itself, it can only perceive the modification of its value. We cannot say which is its absolute value, but only modifications of it. In other words, written as a formula: our perception “p” is detected as a modification of the physical stimulus “m”, when there is a modification in the value of m (Δm) compared to the original value (m). By doing some maths, we reach the final expression. This is known as WEBER'S LAW. This formula is valid for the perception of sound, temperature, time,... Many of the perceptions in our brain behave in this way, in a logarithmic way. There is a threshold for sound intensity (Io). We can’t perceive sounds with an intensity lower than 10^-12 W/m2 = Io (threshold for hearing). Therefore, this value acts as “m”. It’s the physical stimulus whose modification we will be able to perceive. This variation, in mathematical terms, is expressed as the coefficient between the sound intensity which reaches us, and Io (m). Therefore, we recover the Sound level formula: In what units do we measure sound level (𝛽)? Intensity is power divided by Area; therefore, it’s measured in Watts per square metre. To measure sound level, we use the magnitude of decibel (dB). It’s a magnitude of perception. There are lots of different sound levels. Decibel SIL (sound intensity level). Threshold value = 10 to the -12. We can use an alternative way to define sound level: by using the amplitude. Instead of intensity, using amplitude. We will find that this scale is exactly the same as the previous one, but this one is referred to as Decibel SPL (sound pressure level) They are equivalent. THRESHOLD of HEARING Set of sounds we can perceive as a normal person: Frequency / Pitch: from 20 Hz to 20 KHz Sound level /Intensity (dB): When we look at the definition of beta, we see that the minimum value is 0, when I = Io (minimum value in order to hear something). The only possibility is for beta to be positive (above 0, which is the logarithm of 1). The region in blue should be the region where sound is perceived by our ear. But this is not correct. The minimum value needed to trigger a response depends on the frequency, as beta ranges from 0 (when I = Io) to infinity. The red line marks the threshold for hearing. If the incoming sound cannot cross this line, it won’t be heard. This threshold line depends on the person. Is it true that beta can be infinite? NO. This is a pressure wave. At certain pressures, it can produce damage in the inner ear. There is a max intensity that we can inject in the inner ear and is around 120dB. If this line is crossed, we will produce permanent damage to the ear (break the ossicles, eardrum,..) Real diagram: Normal sounds are of the order of 60dB. A quiet room is of the order of 40dB. It’s practically impossible to reach the value of 0 dB Numbers to remember: - 10 ^-12 (Io) = minimum intensity for hearing. Beta = 0 - 120 dB (damage) - Normal range of hearing Lastly, remember a very important point we’ve mentioned. The sound level (perception of sound) is logarithmic, it doesn’t behave in a linear manner. IF MANY PEOPLE ARE TALKING AT THE SAME TIME AT A LEVEL OF 60dB, THE FINAL RESULT IS NOT 60 TIMES THE NUMBER OF PEOPLE. We have to apply the maths to obtain the decibels (intensity) which will be reaching our ear. Logarithmic scale, NOT linear How do we know we are hearing different sounds, even when they have the same pitch? This is so thanks to the “Timbre”.