← Oscillations and wave anatomy

Frequency and the hertz

A ceiling fan's frequency is 4 Hz. Which statement is correct?

Anselm leans on a boardwalk rail, watching a swell train slide past a mooring post. Crest, crest, crest: he starts counting how many pass each second.

That count already has a name in this course. Waves do not get a new quantity here; they re-enter an old one.

Earlier in the course, you met frequency: the number of complete revolutions an object makes each second, measured in hertz, written f.

valvecomplete revolutions each second:frequency f, in hertza spinning bike wheel
Frequency so far: counting a spinning wheel's complete revolutions each second. That count is f, in hertz.

A wave offers the same count. Fix a point, and count the complete waves passing it each second.

The number of complete waves passing a fixed point each second is the wave's frequency: the same quantity f, the same hertz, now counting passing waves instead of revolutions.

If 5 crests pass a buoy each second, the wave's frequency is f = 5 Hz.

rest positionfixed pointtravel direction5 crests pass the post each second: f = 5 Hz
The same count on a wave: five complete waves pass the post each second, so f = 5 Hz.

One complete wave means one full repeat: a crest and the trough that follows it. Counting crests past a point counts complete waves.

Counting for longer than a second still works: count the waves, then divide by the seconds.

Counting for longer still workscrests countedtimefrequency205 s20 ÷ 5 = 4, so f = 4 Hz
Count the waves, then divide by the seconds: 20 ÷ 5 = 4, so f = 4 Hz.

Frequency belongs to how often the wave repeats in time. It says nothing about the wave's height or its length along the water.

One quantity, two countssettingwhat is counted each secondquantityspinning objectcomplete revolutionsfrequency f, in hertz (Hz)passing wavecomplete waves passing a fixed pointthe same frequency f, in the same hertz (Hz)
One quantity, two counts: the same f, in the same hertz, whether it counts revolutions or passing waves.

Beata watches a dock post while ripples pass it. In 5 s, she counts 20 crests passing. Find the wave's frequency.

Frequency counts complete waves passing a fixed point each second.

20 ÷ 5 = 4

f = 4 Hz: four complete waves pass the post each second.

A wave machine's dial reads 9 Hz. Say what the dial's number means at the machine's far wall.

Frequency is the number of complete waves passing a fixed point each second.

The far wall is a fixed point.

Nine complete waves arrive at the far wall each second.

Beata counts 18 crests passing a kayak's bow in 3 s. Enter the wave's frequency in Hz.

A wave crossing a boating lake has a frequency of 7 Hz. What does the 7 say?

Anselm says: 'Wave frequency is measured in hertz, the same unit used for spinning objects earlier in the course.' Is Anselm correct?

Your turn

From a bridge, Cosmo films a piling while swells pass it, and the video shows 32 crests passing in 4 s. Enter the swells' frequency in Hz.

Which measurement gives a wave's frequency?

A wave machine runs at 12 Hz. Which statement is correct?