lumen learning
learning goals
At the end of this section you can:
- Adjust the volume, volume and sound pressure level.
- Calculate the sound intensity levels in decibels (dB).
Sometimes in a silent forest, you can hear a single leaf falling to the ground. After you lie down, you can hear your blood pounding in your ears. But if a passing motorist has their stereo on, you can't even hear what the person next to you is saying. We are all very familiar with the volume of sound and we know that it is related to the intensity with which the source vibrates. In cartoons depicting a person screaming (or an animal making a loud noise), the cartoonist usually shows an open mouth with a vibrating uvula, with the cloth hanging down the back of the mouth to suggest a loud noise. coming from the figure's throat. 2. Exposure to loud noise is dangerous to hearing, and it is common for musicians to have hearing loss severe enough to affect the musician's ability to play. The relevant physical quantity is the intensity of sound, a concept that applies to all sounds, regardless of whether they are in the audible range or not.
Intensity is defined as the power per unit area carried by a wave. Horsepower is the rate at which energy is transferred from the shaft. in equation form,intensity UEEs
, OhPAGis the power over a territoryA. The SI unit forUEes W/m2. The intensity of a sound wave is related to its amplitude squared by the following relationship:
.
Yesterday DPAGis the change in pressure or pressure amplitude (half the difference between the maximum and minimum pressures in the sound wave) in units of Pascal (Pa) or N/m2. (We use lowercase lettersPAGPressure to distinguish it from the power denoted byPAGabove.) Energy (as kinetic energy
) of an air element vibrating due to a moving sound wave is proportional to its amplitude squared. in this equationRis the density of the material through which the sound wave propagates, in units of kg/m3, zvCis the speed of sound in the medium, in units of m/s. The change in pressure is proportional to the amplitude of the oscillation, and soUEvaries as (ΔPAG)2(Figure 2). This relationship agrees with the fact that the sound wave is generated by some vibration; The larger the pressure range, the more air is compressed into the sound produced.
Sound intensity levels are much more commonly expressed in decibels (dB) than sound intensities in watts per square meter. The decibel is the unit of choice in the scientific literature and in the popular media. The reasons for this choice of units are related to the way we perceive sound. The way our ears perceive sound is better described by the logarithm of the volume than by the volume directly. EITHERsound intensity level βin decibels of a sound with intensityUEin watts per square meter is defined as
, OhUE0= 10−12Pm2is a reference intensity. In particular,UE0it is the lowest intensity or threshold of sound that a person with normal hearing can perceive at a frequency of 1000 Hz. The loudness level of sound is not the same as loudness. BecauseBis defined in terms of a proportion, it is a quantity without units that indicates theebenof sound relative to a fixed standard (tenth−12Pm2, In this case). Units in decibels (dB) are used to indicate that this ratio is multiplied by 10 in its definition. The bel on which the decibel is based is named after Alexander Graham Bell, the inventor of the telephone.
| Table 1. Sound intensity levels and intensities | ||
|---|---|---|
| sound intensity levelB(dB) | intensityUE(Pm2) | Example/Effect |
| 0 | 1 × 10–12 | Hearing threshold at 1000 Hz |
| 10 | 1 × 10–11 | rustle of the leaves |
| 20 | 1 × 10–10 | whisper from 1m away |
| 30 | 1 × 10–9 | quiet house |
| 40 | 1 × 10–8 | middle house |
| 50 | 1 × 10–7 | Medium office, soft music |
| 60 | 1 × 10–6 | normal conversation |
| 70 | 1 × 10–5 | Noisy office, lots of traffic |
| 80 | 1 × 10–4 | Loud radio, classroom lecture. |
| 90 | 1 × 10-3 | In a heavy truck; Damage due to prolonged exposure[1] |
| 100 | 1 × 10–2 | Noisy factory, siren at 30 m; 8 hours of damage per day of exposure |
| 110 | 1 × 10–1 | 30 minutes of damage per day of exposure |
| 120 | 1 | Loud rock concert, 2m pneumatic crusher; pain threshold |
| 140 | 1 × 102 | jet planes at 30 m; Intense pain, damage in seconds |
| 160 | 1 × 104 | ruptured eardrum |
The decibel level of a sound with an intensity threshold of 10−12Pm2EsB= 0 dB because log101 = 0. That means the hearing threshold is 0 decibels. Table 1 contains decibel levels and intensities in watts per square meter for some known sounds.
One of the most impressive things about the intensities in Table 1 is that the intensity in watts per square meter is quite small for most sounds. The ear is sensitive to only one billionth of a watt per square meter, which is even more impressive when you consider that the area of the eardrum is only 1 cm.2, then only 10-sixteenW falls on him on the threshold of hearing! The air molecules in a sound wave of this intensity oscillate a distance of less than one molecule diameter, and the pressures involved are less than 10 gauge.–9ATM.
Another impressive feature of the sounds in Table 1 is their numerical range. Sound intensity varies by a factor of 1012from threshold to a sound that deals damage in seconds. You are not aware of these huge fluctuations in sound intensity because the way your ears respond can be roughly described as the logarithm of the volume. Therefore, sound intensity levels measured in decibels are a better fit for your experience than intensities measured in watts per square meter. The decibel scale is also easier to understand since most people are more used to dealing with numbers like 0, 53, or 120 than numbers like 1.00 × 10.–11.
Another observation that can be easily verified by examining Table 1 or using
is that each factor of 10 in volume is equal to 10 dB. For example, compared to a 60 dB tone, a 90 dB tone is 30 dB louder, or three factors of 10 (i.e., 103times) so intense. Another example is when a tone is 107as intense as another, it is 70 dB louder. See Table 2.
| Table 2. Intensity relationships and corresponding differences in sound intensity levels | |
|---|---|
 | B2–B1 |
| 2.0 | 3,0dB |
| 5.0 | 7,0dB |
| 10,0 | 10,0dB |
Example 1. Calculation of sound intensity levels: sound waves
Calculate the sound intensity level in decibels for a sound wave propagating in air at 0°C and having a pressure amplitude of 0.656 Pa.
Strategy
we get ΔPAG, then we can calculateUEusing the equation
. To useUE, we can calculateBdirectly from its definition in.
Solution
1. Identify known: Sound propagates in air at 0°C at 331 m/s. Air has a density of 1.29 kg/m3at atmospheric pressure and 0°C.
2. Enter these values and the pressure range:
3. Enter the value forUEand the known value ofUE0they. To find the sound intensity level in decibels, calculate:
10 records10(5,04 × 108) = 10(8,70)dB = 87dB.
discussion
This 87 dB tone is five times louder than an 80 dB tone. Therefore, a factor of five in volume corresponds to a difference of 7 dB in the volume level of the sound. This value applies to all intensities that differ by a factor of five.
Example 2. Changing the volume of a tone: What happens to the decibel level?
Show that one sound twice as loud as another has a sound level about 3 dB higher.
Strategy
You know that the ratio of two intensities is 2 to 1 and then you are asked to find the difference in their sound levels in decibels. You can solve this problem using the properties of logarithms.
Solution
1. Identify acquaintances.
The ratio of the two intensities is 2 to 1, or:
.
We want to show that the sound level difference is about 3 dB. That means we want to show
B2−B1= 3 dB.
Realise
.
2. Use the definition ofBreceive:
For this reason,
B2−B1= 3,01dB.
discussion
This means that the two sound intensity levels differ by 3.01 dB, or about 3 dB as indicated. Consider that alone as the reason(rather than actual intensities), this result holds for all intensities that differ by a factor of two. For example, a 56.0 dB tone is twice as loud as a 53.0 dB tone, a 97.0 dB tone is half as loud as a 100 dB tone, and so on.
It should be noted at this point that another decibel scale is used called the decibel.sound pressure level, based on the relationship between the pressure amplitude and a reference pressure. This scale is mainly used in applications where sound travels through water. It is beyond the scope of most introductory texts to deal with this scale, as it is not commonly used for airborne noise, but it is important to note that very different decibel values can be found when reporting levels. of sound pressure. For example, marine noise pollution from ships can be as high as 200 dB expressed as a sound pressure level, where the more familiar sound intensity level we use here would be just under 140 dB for the same sound.
Takeaway Research: Feel the Sound
Find a CD player and a rock music CD. Place the player on a light table, insert the CD into the player, and start playing the CD. Place your hand gently on the table next to the speakers. Turn up the volume and watch the level as the table starts to vibrate while rock music is playing. Increase the value on the volume slider until it doubles. What happened to the vibrations?
check your understanding
Part 1
Describe how amplitude is related to the volume of a tone.
Solution
The amplitude is directly proportional to the volume experience. As the amplitude increases, the loudness increases.
Part 2
Identify common noises at 10dB, 50dB and 100dB.
Solution
10dB: Run your fingers through your hair.
50 dB: In a quiet house, without TV or radio.
100 dB: takeoff of a jet plane.
summary section
- The intensity is the same for a sound wave defined for all waves; that's all
, OhPAGis the energy transition areaA. The SI unit forUEis watts per square meter. The intensity of a sound wave is also related to the amplitude of the pressure ΔPAG,, OhRis the density of the medium in which the sound wave propagates andvCis the speed of sound in the medium. - The sound intensity level in units of decibels (dB).,where0= 10–12Pm2is the hearing intensity threshold.
, OhRis the density of the medium in which the sound wave propagates andvCis the speed of sound in the medium.
,where0= 10–12Pm2is the hearing intensity threshold.conceptual problems
- Six members of a synchronized swimming team wear earplugs to protect themselves from water pressure at depth, but can still hear the music and perform combinations perfectly in the water. One day they were asked out of the pool so the dive team could practice a few dives and they tried to practice on a mat but seemed to have a lot more trouble. Why can this be?
- A community is concerned about a plan to move rail service from the outskirts of the city to the center of the city. The current sound intensity level is 70 dB in the city center, even though the rail yard is only a few blocks away. The mayor assures the public that there will only be a 30 dB difference in sound in the center of the city. Do city dwellers need to worry? Because?
Problems and Exercises
- What is the intensity in watts per square meter of the 85.0 dB sound?
- The warning label on a lawn mower states that it makes a noise of 91.0 dB. How much is that in watts per square meter?
- A sound wave propagating in air at 20°C has a pressure amplitude of 0.5 Pa. How strong is the wave?
- What is the intensity of the sound in the above task?
- What sound intensity in dB is produced by headphones that produce an intensity of 4.00 × 10−2Pm2?
- Show that an intensity of 10−12Pm2is equal to 10−16Pm2.
- (a) What is the decibel level of a sound twice as loud as a 90.0 dB sound? (b) What is the decibel level of a sound that is one-fifth the intensity of a 90.0 dB sound?
- (a) What is the intensity of a sound that is 7.00 dB smaller than 4.00 × 10−9Pm2Sound? (b) What is the intensity of a tone that is 3.00 dB greater than a 4.00 × 10 tone?−9Pm2and?
- (a) How much louder is a sound that is 17.0 dB louder than another sound? (b) If one sound has a level 23.0 dB lower than another, what is the ratio of their intensities?
- People with good hearing can hear sounds as low as -8.00 dB at a frequency of 3000 Hz. What is the intensity of this noise in watts per square meter?
- If a large housefly 3.0 m from you makes a noise of 40.0 dB, what is the noise level of 1000 houseflies at that distance if the disturbance has negligible effect?
- Ten cars in a circle in a boombox competition produce a sound intensity level of 120 dB at the center of the circle. What is the average sound intensity level produced by each stereo system, assuming that interference effects can be neglected?
- The amplitude of a sound wave is measured in relation to its maximum gauge pressure. By what factor does the amplitude of a sound wave increase when the sound intensity level increases by 40.0 dB?
- If a sound intensity level of 0 dB at 1000 Hz corresponds to a maximum gauge pressure (sound amplitude) of 10−9atm, what is the maximum overpressure with a sound of 60 dB? What is the maximum overpressure with a sound of 120 dB?
- Exposure to a sound intensity of 90.0 dB for 8 hours can damage your hearing. What energy in joules strikes an exposed eardrum with a diameter of 0.800 cm?
- (a) Trumpets were never very common, but they helped people with hearing loss by collecting sound in a large area and focusing it on the smaller area of the eardrum. What decibel increase does a trumpet produce if its sound pickup range is 900 cm?2and the area of the tympanic membrane is 0.500 cm.2, but the trumpet only has a 5.00% efficiency in transmitting sound to the eardrum? (b) Comment on the usefulness of the decibel increase found in part (a).
- Sound is more effectively transmitted to a stethoscope through direct contact than through air, and is further intensified by focusing on the smaller area of the eardrum. It can be assumed that sound is transmitted 100 times more effectively through a stethoscope than through air. What then is the gain in decibels produced by a stethoscope with a sound pickup area of 15.0 cm?2, and concentrates the sound in two eardrums with a total area of 0.900 cm2with an efficiency of 40.0%?
- Despite their low efficiency, the speakers can produce rich sounds with surprisingly low power consumption. Calculate the input power required to produce a sound intensity level of 90.0 dB for a 12.0 cm diameter speaker with 1.00% efficiency. (This value is the volume level of the sound directly into the speaker.)
glossary
Intensity:the power per unit area carried by an axle
Sound intensity level:a unitless quantity indicating the sound level relative to a fixed standard
Sound pressure level:the relationship between the pressure amplitude and a reference pressure
Selected solutions to problems and exercises.
1. 3,16 × 10−4Pm2
3.3.04 × 10−4Pm2
5,106dB
7.(a) 93dB;(b) 83dB
9.(a) 50,1;(b) 5,01 × 10−3o
11,70,0dB
13.100
15.1.45 × 10−3j
17,28,2dB
- Several government agencies and professional health organizations recommend that 8-hour daily exposures not exceed 85 dB without hearing protection.↵