Physics Equations
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Pressure (pascals) =
 Force (Newtons)
 ______________
 area (cm²)

Relationship between frequency and period
they are reciprocals
Period(s) = 1/frequency(Hz)
Frequency(Hz) = 1/period(s)


Relationship between power and amplitude
Power (W) = Amplitude² (dB²)

Intensity (W/cm^{2})=
 Power (W)
 _______________
 beam area (cm^{2})

Wavelength (mm) =
 Propagation Speed (mm/μs)
 ________________________________
 frequency (MHz)

Wavelength in Soft Tissue =
 1.54 mm/μs
 _______________
 frequency (MHz)

Speed (m/s)=
frequency (Hz) x Wavelength (m)

Pulse duration (μsec)=
cycles in a pulse x period (μsec)

Pulse duration (μsec) =
 # of cycles in a pulse
 __________________
 frequency (MHz)


Relationship between Pulse Repetition Period (sec) and Pulse Repetition Frequency (Hz)

Duty Factor(%) =
 Pulse Duration (msec)
 _________________________ x 100
 Pulse Repetition Period (msec)

Spatial Pulse Length (mm) =
# of cycles x wavelength (mm)

Total Attenuation (dB) =
path length (cm) x attenuation coefficient (dB/cm)

Impedance (Rayls) =
Density (kg/cm^{3}) x propagation speed (m/s)

Incident Intensity (dB/cm^{2}) =
reflected intensity + transmitted intensity

Intensity reflection coefficient (%) =
 Z_{2 } Z_{1}
 (________ ) ^{2 OR}
 Z_{2 }+ Z1
[(Z
_{2}Z
_{1})/ (Z
_{2}+Z
_{1})]
^{2}

Incident transmission coefficient (%) =
 Transmitted Intensity
 __________________ x 100
 Incident Intensity

Intensity Transmission Coefficient (%) =
100%  Intensity Reflection Coefficient

Transmitted Intensity =
Incident Intensity x Intensity Transmission Coefficient

Snell's Law:
 sin (angle of transmission) propg. speed 2
 _____________________ = ______________
 sin (angle of incidence) propg. speed 1

Frequency (Hz) =
attenuation coefficient x 2

distance to boundary (mm) =
 goreturn time (μs) x speed (mm/μs)
 ________________________________
 2

Bandwidth =
Maximum Frequency  Minimum Frequency

Quality Factor =
 resonant frequency (MHz)
 ______________________
 bandwidth (MHz)

Frequency of a Pulsed Transducer (MHz) =
 material's propagation speed (mm/μs)
 ________________________________
 2x thickness (mm)

Attenuation coefficient (dB/cm^{2})=
1/2 Frequency (MHz)

To find the depth or time of flight in soft tissue:
 depth = 1.54 (mm/μs) x goreturn time (μs)
 _____________________________
 2

Pulse Repetition Period in soft tissue (μs) =
imaging depth (cm) x 13(μs/cm)

Pulse Repetition Frequency in soft tissue (Hz) =
 77,000 (cm/s)
 _________________
 imaging depth (cm)

Time of flight (μs) =
depth (cm) x 13μs

Axial Resolution (mm) =
 spatial pulse length (mm)
 ______________________
 2

Axial Resolution (mm) =
 0.77 x # of cycles in pulse
 ______________________
 frequency (MHz)

