# 17.3 Sound intensity and sound level  (Page 2/7)

 Page 2 / 7
$\beta \phantom{\rule{0.25em}{0ex}}\left(\text{dB}\right)=\text{10}\phantom{\rule{0.25em}{0ex}}{\text{log}}_{\text{10}}\left(\frac{I}{{I}_{0}}\right),$

where ${I}_{0}={\text{10}}^{\text{–12}}\phantom{\rule{0.25em}{0ex}}{\text{W/m}}^{2}$ is a reference intensity. In particular, ${I}_{0}$ is the lowest or threshold intensity of sound a person with normal hearing can perceive at a frequency of 1000 Hz. Sound intensity level is not the same as intensity. Because $\beta$ is defined in terms of a ratio, it is a unitless quantity telling you the level of the sound relative to a fixed standard ( ${\text{10}}^{\text{–12}}\phantom{\rule{0.25em}{0ex}}{\text{W/m}}^{2}$ , in this case). The units of decibels (dB) are used to indicate this ratio is multiplied by 10 in its definition. The bel, upon which the decibel is based, is named for Alexander Graham Bell, the inventor of the telephone.

Sound intensity levels and intensities
Sound intensity level β (dB) Intensity I (W/m 2 ) Example/effect
$0$ $1×{10}^{–12}$ Threshold of hearing at 1000 Hz
$10$ $1×{10}^{–11}$ Rustle of leaves
$20$ $1×{10}^{–10}$ Whisper at 1 m distance
$30$ $1×{10}^{–9}$ Quiet home
$40$ $1×{10}^{–8}$ Average home
$50$ $1×{10}^{–7}$ Average office, soft music
$60$ $1×{10}^{–6}$ Normal conversation
$70$ $1×{10}^{–5}$ Noisy office, busy traffic
$80$ $1×{10}^{–4}$ Loud radio, classroom lecture
$90$ $1×{10}^{–3}$ Inside a heavy truck; damage from prolonged exposure Several government agencies and health-related professional associations recommend that 85 dB not be exceeded for 8-hour daily exposures in the absence of hearing protection.
$100$ $1×{10}^{–2}$ Noisy factory, siren at 30 m; damage from 8 h per day exposure
$110$ $1×{10}^{–1}$ Damage from 30 min per day exposure
$120$ $1$ Loud rock concert, pneumatic chipper at 2 m; threshold of pain
$140$ $1×{10}^{2}$ Jet airplane at 30 m; severe pain, damage in seconds
$160$ $1×{10}^{4}$ Bursting of eardrums

The decibel level of a sound having the threshold intensity of ${\text{10}}^{–\text{12}}\phantom{\rule{0.25em}{0ex}}{\text{W/m}}^{2}$ is $\beta =0\phantom{\rule{0.25em}{0ex}}\text{dB}$ , because ${\text{log}}_{\text{10}}1=0$ . That is, the threshold of hearing is 0 decibels. [link] gives levels in decibels and intensities in watts per meter squared for some familiar sounds.

One of the more striking things about the intensities in [link] is that the intensity in watts per meter squared is quite small for most sounds. The ear is sensitive to as little as a trillionth of a watt per meter squared—even more impressive when you realize that the area of the eardrum is only about ${1 cm}^{2}$ , so that only ${\text{10}}^{–\text{16}}$ W falls on it at the threshold of hearing! Air molecules in a sound wave of this intensity vibrate over a distance of less than one molecular diameter, and the gauge pressures involved are less than ${\text{10}}^{–9}$ atm.

Another impressive feature of the sounds in [link] is their numerical range. Sound intensity varies by a factor of ${\text{10}}^{\text{12}}$ from threshold to a sound that causes damage in seconds. You are unaware of this tremendous range in sound intensity because how your ears respond can be described approximately as the logarithm of intensity. Thus, sound intensity levels in decibels fit your experience better than intensities in watts per meter squared. The decibel scale is also easier to relate to because most people are more accustomed to dealing with numbers such as 0, 53, or 120 than numbers such as $1\text{.}\text{00}×{\text{10}}^{–\text{11}}$ .

One more observation readily verified by examining [link] or using $I={\frac{\left(\Delta p\right)}{2{\text{ρv}}_{\text{w}}}}^{2}$ is that each factor of 10 in intensity corresponds to 10 dB. For example, a 90 dB sound compared with a 60 dB sound is 30 dB greater, or three factors of 10 (that is, ${\text{10}}^{3}$ times) as intense. Another example is that if one sound is ${\text{10}}^{7}$ as intense as another, it is 70 dB higher. See [link] .

how do you calculate the 5% uncertainty of 4cm?
4cm/100×5= 0.2cm
haider
how do you calculate the 5% absolute uncertainty of a 200g mass?
= 200g±(5%)10g
haider
use the 10g as the uncertainty?
melia
haider
topic of question?
haider
the relationship between the applied force and the deflection
melia
sorry wrong question i meant the 5% uncertainty of 4cm?
melia
its 0.2 cm or 2mm
haider
thank you
melia
the meaning of phrase in physics
is the meaning of phrase in physics
Chovwe
write an expression for a plane progressive wave moving from left to right along x axis and having amplitude 0.02m, frequency of 650Hz and speed if 680ms-¹
how does a model differ from a theory
To use the vocabulary of model theory and meta-logic, a theory is a set of sentences which can be derived from a formal model using some rule of inference (usually just modus ponens). So, for example, Number Theory is the set of sentences true about numbers. But the model is a structure together wit
Jesilda
with an iterpretation.
Jesilda
what is vector quantity
Vector quality have both direction and magnitude, such as Force, displacement, acceleration and etc.
Besmellah
Is the force attractive or repulsive between the hot and neutral lines hung from power poles? Why?
what's electromagnetic induction
electromagnetic induction is a process in which conductor is put in a particular position and magnetic field keeps varying.
Lukman
wow great
Salaudeen
what is mutual induction?
je
mutual induction can be define as the current flowing in one coil that induces a voltage in an adjacent coil.
Johnson
how to undergo polarization
show that a particle moving under the influence of an attractive force mu/y³ towards the axis x. show that if it be projected from the point (0,k) with the component velocities U and V parallel to the axis of x and y, it will not strike the axis of x unless u>v²k² and distance uk²/√u-vk as origin
show that a particle moving under the influence of an attractive force mu/y^3 towards the axis x. show that if it be projected from the point (0,k) with the component velocities U and V parallel to the axis of x and y, it will not strike the axis of x unless u>v^2k^2 and distance uk^2/√u-k as origin
No idea.... Are you even sure this question exist?
Mavis
I can't even understand the question
yes it was an assignment question "^"represent raise to power pls
Gabriel
Gabriel
An engineer builds two simple pendula. Both are suspended from small wires secured to the ceiling of a room. Each pendulum hovers 2 cm above the floor. Pendulum 1 has a bob with a mass of 10kg . Pendulum 2 has a bob with a mass of 100 kg . Describe how the motion of the pendula will differ if the bobs are both displaced by 12º .
no ideas
Augstine
if u at an angle of 12 degrees their period will be same so as their velocity, that means they both move simultaneously since both both hovers at same length meaning they have the same length
Modern cars are made of materials that make them collapsible upon collision. Explain using physics concept (Force and impulse), how these car designs help with the safety of passengers.
calculate the force due to surface tension required to support a column liquid in a capillary tube 5mm. If the capillary tube is dipped into a beaker of water
find the time required for a train Half a Kilometre long to cross a bridge almost kilometre long racing at 100km/h
method of polarization
Ajayi
What is atomic number?
The number of protons in the nucleus of an atom
Deborah