Ultrasound Physics Formulas/Relationships

Formula for Period and Frequency

p x f =1

How are Period and Frequency related?

inversely & reciprocals

Formula for Power and Amplitude²

Power is proportional to Amplitude²

How are Power and Amplitude² related?

directly

Formula for Intensity

Intensity (W/cm²) = power (W)/area (cm²)

Relation ship between Intensity and Power

directly and proportional

Relationship between Intensity and Amplitude²

directly and proportional

Formula for Wavelength

wavelength(mm) = 1.54(mm/us) / frequency (MHz)

How are Wavelength and Frequency related?

inversely

Formula for Propagation Speed

speed(m/s) = frequency(Hz) x wavelength(m)

How are speed, frequency, and wavelength related?

All directly related

First formula for Pulse Duration

PD(us) = # of cycles x period(us)

Second formula for Pulse Duration

PD(us) = # of cycles / frequency(MHz)

How are Pulse Duration and # of cycles related?

directly

How are Pulse Duration and Period related?

directly

How are Pulse Duration and Frequency related?

inversely

How are stiffness and speed related?

directly

Hoare are density and speed related?

inversely

Formula for Spatial Pulse Length

SPL(mm) = # of cycles x wavelength (mm)

How are Spatial Pulse Length and # of cycles related?

directly

How are Spatial Pulse Length and wavelength related?

directly

How are Spatial Pulse Length and frequency related?

inversely

Relationship between PRP and Period

unrelated

How are PRP and Imaging depth related?

directly

Relationship between PRF and Frequency?

unrelated

How are PRF and Imaging depth realted

inversely

Relationship between PRP and PRF?

inversely & reciprocals

Formula for PRP and PRF

PRP x PRF =1

Formula for Duty Factor

DF(%) = pulse duration / PRP x 100

Relationship between DF and PRP?

inversely

Relationship between DF and PRF?

directly

Formula for Rayleigh Scattering

rayleigh is proportional to frequency⁴

What is the relationship between Rayleigh scattering and frequency?

directly

First formula for Attenuation Coefficient

total attenuation(dB) = atten. coefficient(dB/cm) x distance (cm)

Second formula for Attenuation Coefficient

total attenuation(dB) = F/2 x distance

First formula for Attenuation Coefficient in Soft Tissue

attenuation coefficiente(dB/cm) = frequency(MHz) / 2

Second formula for Attenuation Coefficient in Soft Tissue

attenuation coefficient = 0.5db/cm/MHz

How are scattering and absorption related to frequency?

directly

Formula for Impedance

impedance(rayls) = density(kg/m³) x propogation speed

The formula for Incident, Reflected, and Transmitted sound

incident (starting) intensity = reflected intensity + transmitted intensity

What is the units for all intestines?

W/cm²

Formula for IRC and ITC

100% = IRC(%) + ITC(%)

First formula for Transmission with Normal Incidence

ITC(%) = transmitted intensity / incident intensity x 100

Second formula for Transmission with Normal Incidence

ITC(%) 1 - intensity reflection coefficient

Formula for Conservation of Energy

100% = reflection coefficient + transmission coefficient

Second formula for Conservation of Energy

Incident intensity(W/cm²) = reflected intensity + transmitted intensity

Formula for Snell's law

sin (transmission angle) / sin (incident angle) = speed of Medium 2 / speed of Medium 1

Formula for Death of Reflector

depth(mm) = 1.54(mm/us) x go-return time(us) / 2

Formula for PRP and Max imaging depth

PRP(us) = imaging depth(cm) x 13(us/cm)

Relationship between PRP and Max imaging depth

directly

Formula for PRF and Max imaging depth

PRF(HZ) = 77,000(cm/s) / imaging depth(cm)

Relationship between PRF and Max imaging depth

inversely

Formula for Low Quality Factor

quality factor = main frequency / bandwidth

The relationship between quality and pulse length?

directly

Formula for Continuous Wave Transducers

electrical frequency = acoustic frequency

Formula for PZT thickness and Frequency

frequency(MHZ) = sound's speed in PZT(mm/us) / 2 x thickness

The relationship of the PZT thickness and frequency?

inversely

Formula for focal depths

focal depth(mm) = diameter(mm)² x frequency(MHz) / 6

Another formula for focal depth

focal depth(mm) = diameter(mm)² / 4 x wavelength(mm)

Formula for transducer diameter, frequency, and beam divergence

sin divergence angle = 1.85 / diameter(mm) x frequency(MHz)

Another formula for transducer diameter, frequency, and beam divergence

sin divergence angle = 1.2 x wavelength / diameter

First formula for Axial Resolution and image quality

axial resolution(mm) = spatial pulse length(mm) / 2

Second formula for Axial Resolution and image quality

axial resolution(mm) = wavelength(mm) x # of cycles in pulse / 2

Formula for Axial Res in soft tissue

axial resolution(mm) = 0.77 x #cycles in pulse / frequency(MHz)

Formula for Lateral Resolution

lateral resolution = beam diamete(mm)