Motion toward Transducer Raises Frequency - Biophysical Ultrasound: Echo Timing and Acoustic Interfaces Step by Step

Doppler shift is a signed frequency budget. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Along-beam motion gives a signed shift

Transmit frequency 6 hertz, speed 1 meter per second, and sound speed 3 meters per second give shift 4 hertz.

\Delta f=\frac{2\cdot 6\cdot 1}{3}=4\ \text{Hz}

The sign convention is part of the checked model

The motion is toward the transducer, so the signed shift is positive 4 hertz in this training ledger.

\Delta f=+4\ \text{Hz}