What are the dimensional units for intensity of wave?
Answers
Answer:
Amplitude, intensity, and loudness are often used interchangeably, but the three terms have different meanings.
Amplitude is a measure of the maximal change in whatever quantity is varying in a wave.
For sound waves, the varying quantity [and its SI unit] could be…
position [m]
velocity [m/s]
acceleration [m/s2]
pressure [Pa]
density [kg/m3]
Position and density variations caused by sound waves are difficult to measure directly since…
their magnitudes are small and
the period of sound waves are brief.
Pressure variations caused by sound waves can be detected…
by animals with their ears and
by machines with microphones
Intensity is an objective measure of the time-averaged power density of a wave at a particular location.
The SI unit of intensity is the watt per square meter.
As an equation, intensity is defined as…
I = ⟨P⟩
A
Where…
I = intensity
⟨P⟩ = time-averaged power
A = area through which the wave is propagating in a plane perpendicular to the direction of propagation
When the amplitude of a sound wave is measured by the maximum displacement of the particles that make up the medium, its intensity is equal to…
I = 2π2ρf2v∆s2 Where…
I = intensity
Δs = maximum displacement of particles in the medium (displacement amplitude)
ρ = density of medium
f = wave frequency
v = wave speed
When the amplitude of a sound wave is measured by the maximum gauge pressure of the medium in bulk, its intensity is equal to…
I = ∆P2
2ρv
Where…
I = intensity
∆P = maximum gauge pressure (pressure amplitude)
ρ = density of medium
v = wave speed
When the amplitude of a sound wave is measured by the maximum change in density of the medium in bulk, its intensity is equal to…
I = ∆ρ2v3
2ρ
Where…
I = wave intensity
Δρ = maximum density change (density amplitude)
ρ = density of medium
v = wave speed
The level (L) of a quantity is the logarithm of the quantity compared to a reference value for the quantity.
When the logarithm used is base ten, the SI unit is the bel (B).
Although the bel is computed from quantities with units, the bel is itself unitless.
The bel is too big for most purposes so the decibel (dB) is more common.
1 bel = 10 decibel
A level increase of 3 dB is approximately equal to a doubling of intensity (since log 2 ≈ 0.3).
Sound level values are typically computed using intensity or pressure amplitude.
The equation for sound intensity level (often abbreviated SIL) in decibels is…
LI = 10 log ⎛
⎝ I ⎞
⎠
I0
where…
LI = sound intensity level [dB]
I = intensity [W/m2]
I0 = reference intensity [W/m2]
The equation for sound pressure level (often abbreviated SPL) in decibels is…
LP = 20 log ⎛
⎝ ∆P ⎞
⎠
∆P0
where…
LP = sound pressure level [dB]
∆P = maximum gauge pressure or pressure amplitude [W/m2]
∆P0 = reference gauge pressure [W/m2]
The standard reference values for sounds are defined from pressure amplitudes.
By definition, a pressure amplitude of 20 µPa in air corresponds to a sound pressure level of 0 dB.
By definition, a pressure amplitude of 1 µPa in water corresponds to a sound pressure level of 0 dB.
Levels are also commonly used for quantities in audio electronics, radio transmission, and other branches of science and engineering.
Loudness is…
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Intensity
… sound
intensity
doppler-sound …
Explanation: