Reciprocals

When you multiply two numbers and the result equals one, those numbers are reciprocals.

Reciprocals are inversely related. When one goes up, the other goes down.

Imagine you have exactly one full glass of water to split between two glasses. Drag glass A up to pour more into it. Watch what happens to glass B.

Glass A
1/2
×
Glass B
2
1/2 × 2 = 1
Drag glass A up or down

No matter how you split it, when you multiply them together, the answer is always one. That is what makes them reciprocals.

Tap a number to see its reciprocal. Notice: they always multiply to one.

Tap a number above

To find a reciprocal, just flip the fraction. The reciprocal of 2 (which is 2/1) is 1/2. Flip the top and bottom.

In ultrasound, period and frequency are reciprocals. They multiply to equal one, and they are inversely related.

2 MHz
Frequency
×
0.5 µs
Period
=
1
Always
Tap the wave to change frequency

When frequency increases, period decreases. They are reciprocals and inversely related. You will use this relationship throughout ultrasound physics.

Frequency
Definition: How many cycles per second.

The reciprocal of period. Frequency = 1 / Period.
Period
Definition: How long one complete cycle takes.

The reciprocal of frequency. Period = 1 / Frequency.

Quick Check

What do two reciprocals always multiply to?
What is the reciprocal of 4?
Period and frequency are reciprocals. If frequency doubles, what happens to period?