IMG-17

Ultrasound depth z = ct/2

z = c t / 2 with c ≈ 1540 m/s in soft tissue. Round-trip ranging.

Reading speed

UltrasoundPulse-echo

Governing equation

z=ct/2

where

c: Speed of sound (m/s)
t: Round-trip time (µs)
z: Depth (cm)

Lecture brief

Historical brief

Larmor precession, CT Beer projections, SNR and Nyquist sampling are why MRI and CT images exist as numbers. The lab computes frequency, dose and resolution limits. This sheet (IMG-17 — Ultrasound depth z = ct/2) is the form associated with Pulse-echo. Working symbols: $c$ , $t$ $\rightarrow$ $z$ . 13 μs per centimetre of depth is the sonographer's rule (because 1540 m/s × 13 μs / 2 ≈ 1 cm).

Purpose

Purpose: compute

z

from

c

t

in Medical imaging via

z=ct/2

z = c t / 2 with c ≈ 1540 m/s in soft tissue. Round-trip ranging. Use it when a real medical imaging question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

c = 1540.000\,\mathrm{m/s}

t = 130.000\,\mathrm{\mu s}

, the governing relation

z=ct/2

yields

z = 10.01\,\mathrm{cm}

. A pulse going out and an echo coming home. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Speed of sound c1540 m/sRound-trip time t130 µs

Outputs

Depth z10.01 cm

Reading speed

Watch on YouTube

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Narration of this film

A pulse going out and an echo coming home.

13 μs per centimetre of depth is the sonographer's rule (because 1540 m/s × 13 μs / 2 ≈ 1 cm).

Reading speed

Watch on YouTube