Ultrasound Relation Cross Scans

Intensity Square Three-Row Scan

Intensity reflection uses the square of the pressure ratio. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Intensity uses the square of the pressure ratio

The scan changes the pressure ratio and then squares it before multiplying intensity.

Ir=R2IiI_r=R^2I_i
Intensity square rowThe intensity label is checked after the square.incidentreflectedtransmittedleft 2 raylright 6 raylR 1/2in 8 Paback 4 Pathrough 12 PaI back 4 W/m^2

Three amplitude ratios become square intensity fractions

The same incident intensity gives one, four, and nine reflected intensity units.

RR⋅RIiIr14116161121416434916169\begin{array}{c|c|c|c}R&R\cdot R&I_i&I_r\\\frac{1}{4}&\frac{1}{16}&16&1\\\frac{1}{2}&\frac{1}{4}&16&4\\\frac{3}{4}&\frac{9}{16}&16&9\\\end{array}

The middle row squares one half into one quarter

The sign would disappear here because intensity uses the square.

16⋅14=416\cdot\frac{1}{4}=4
Reflected intensity from ratioThe reflected intensity is bound to the squared ratio.incidentreflectedtransmittedleft 2 raylright 6 raylR 1/2in 8 Paback 4 Pathrough 12 PaI back 4 W/m^2