User:


Mecanismo

Storyboard

ID:(806, 0)


Pulse propagating

Image

The pulse propagates through a homogeneous medium in a rectilinear way:

ID:(7829, 0)


Transmitted and reflected pulse

Image

The pulse is partially transmitted and reflected at the interface where the speed of propagation undergoes a change:

ID:(7830, 0)


Impedance in waves

Equation

To calculate impedance ($Z$) from the mean density ($\rho$) and the speed of sound ($c$), the formula used is:

$ Z = \rho c $

$Z$
Impedance
$kg/m^2s$
$\rho$
Mean density
$kg/m^3$
$c$
Speed of sound
$m/s$

Since impedance ($Z$) is calculated from the sound pressure ($p$) and the molecule speed ($u$) using

$ Z =\displaystyle\frac{ p }{ u }$



along with the expression for the sound pressure ($p$) in terms of the mean density ($\rho$) and the speed of sound ($c$),

$ p = \rho c u $



we obtain

$ Z = \rho c $

ID:(12413, 0)


Transmitted Factor

Equation

If the impedance of one medium is Z_1 and of the second Z_2 the transmitted fraction of the sound wave will be

$ T_{12} =\displaystyle\frac{2\sqrt{ Z_1 Z_2 }}{ Z_1 + Z_2 }$

$Z_1$
Impedance in Medium 1
$kg/m^2s$
$Z_2$
Impedance in Medium 2
$kg/m^2s$
$T_{12}$
Transfer Factor
$-$

ID:(4130, 0)


Transmission factor

Image

The transmission factor

$ T_{12} =\displaystyle\frac{2\sqrt{ Z_1 Z_2 }}{ Z_1 + Z_2 }$



can be plotted as a function of the ratio of the impedance in the medium that is transmitted divided by the impedance of the medium from which it comes:

ID:(14210, 0)


Amplitude Transmitted

Equation

Si una onda que amplitud A_1 se propaga en un medio 1 arriba a una interface con un segundo medio 2, la amplitud transmitida A_2 se puede calcular del factor de transmisión T_{12} de la forma

$ A_t = T_{12} A_i $

$A_i$
Amplitude
$m$
$A_t$
Amplitude Transfer
$m$
$T_{12}$
Transfer Factor
$-$

Es importante hacer notar que en el proceso de transmisión el signo de la amplitud permanece inalterado, y como el factor de transmisión es siempre menor a uno, puede sufrir una reducción.

ID:(4118, 0)


Reflection Factor

Equation

If the impedance of one medium is Z_1 and of the second Z_2 the reflected fraction of the sound wave will be

$ R_{12} =\displaystyle\frac{ Z_1 - Z_2 }{ Z_1 + Z_2 }$

$Z_1$
Impedance in Medium 1
$kg/m^2s$
$Z_2$
Impedance in Medium 2
$kg/m^2s$
$R_{12}$
Reflection Factor
$-$

ID:(4117, 0)


Reflection factor

Image

The reflection factor

$ R_{12} =\displaystyle\frac{ Z_1 - Z_2 }{ Z_1 + Z_2 }$



can be plotted as a function of the ratio of the impedance in the medium that is transmitted divided by the impedance of the medium from which it comes:

ID:(14211, 0)


Reflected Amplitude

Equation

Si una onda que amplitud A_1 se propaga en un medio 1 arriba a una interface con un segundo medio 2, la amplitud reflejada A_2 se puede calcular del factor de reflexión R_{12} de la forma

$ A_r = R_{12} A_i $

$A_i$
Amplitude
$m$
$A_r$
Amplitude Reflected
$m$
$R_{12}$
Reflection Factor
$-$

Es importante hacer notar que en el proceso de reflexión el signo de la amplitud puede invertirse debido a que R_{12} puede asumir valores negativos. Sin embargo, el módulo del factor de reflexión es siempre menor a uno, por lo que la amplitud puede sufrir además una reducción.

ID:(4129, 0)


0
Video

Video: Mecanismo