The pond ripple again: a crest travels 6 m in 2 s, so following it with a stopwatch gives 6 ÷ 2 = 3, a speed of 3 m/s.
Here is a second route to that same 3 m/s, with no walking and no stopwatch run. Stand at one spot, count, and measure.
Stand at one spot on the pond. Crests pass at 2 each second: the wave's frequency is 2 Hz.
Measure the gap between neighboring crests: 1.5 m. That is the wavelength.
Each second, 2 crests pass, and each crest moves the pattern on by one gap of 1.5 m. So the pattern advances 2 × 1.5 = 3 m each second.
That is 3 m/s: exactly the stopwatch answer. The two routes must agree, because both measure how far the pattern moves each second.
The symbols, each with its unit: v = wave speed (m/s). f = frequency (Hz). λ = wavelength (m).
The units combine the way the counting did. Hz means per second, so multiplying per-second by meters gives meters per second: m/s, a speed's unit.
This is speed = distance ÷ time rewritten in wave-friendly quantities: new notation, zero new physics. And it is the one written form; when the speed is known and the frequency or the wavelength is wanted, this same equation is rearranged, never replaced by a new formula.
On a lake, 4 crests pass a dock post each second, and neighboring crests are 0.9 m apart. Calculate the wave's speed.
Write down the values:
f = 4 Hz, λ = 0.9 m, v = ?
Write down the equation:
v = fλ
Substitute in the values, and calculate:
v = 4 × 0.9 = 3.6
The wave's speed is 3.6 m/s.
A machine sends waves down a long cord: 8 waves each second, with neighboring crests 0.7 m apart. Calculate the wave's speed.
Write down the values:
f = 8 Hz, λ = 0.7 m, v = ?
Write down the equation:
v = fλ
Substitute in the values, and calculate:
v = 8 × 0.7 = 5.6
The wave's speed is 5.6 m/s.
On a rope, 5 waves pass a marker each second, and neighboring crests are 1.4 m apart. Enter the wave's speed, in m/s.
A wave has frequency 4 Hz and wavelength 2.5 m. Which calculation gives its speed?
Hale says: 'Multiplying how many crests pass each second by the distance between crests gives how far the wave pattern travels each second.' Is Hale correct?
In a ripple tank, the dipper bobs 8 times each second, and neighboring crests are 0.06 m apart. Enter the wave's speed, in m/s.
Why does multiplying a wave's frequency by its wavelength give its speed?
A long jump rope carries waves: the turner's hand vibrates 2.5 times each second, and neighboring crests are 1.8 m apart. Enter the wave's speed, in m/s.