Lesson 4 of 6
Wave speed, frequency and wavelength
I can use displacement, amplitude, period, frequency, phase, phase difference, wavelength and wave speed.Syllabus
Syllabus 9478, 10(b). Use displacement, amplitude, period, frequency, phase, phase difference, wavelength and wave speed.
I can deduce v = f lambda from the definitions of speed, frequency and wavelength.Syllabus
Syllabus 9478, 10(c). Deduce v = f lambda from the definitions of speed, frequency and wavelength.
I can recall and use v = f lambda.Syllabus
Syllabus 9478, 10(d). Recall and use v = f lambda.
Wave speed measures how quickly a phase feature progresses. In one period, that feature travels one wavelength, connecting speed to frequency and wavelength.
Wavelength λ is the distance between neighbouring points in the same phase at one instant. Period T is the repeat time at a fixed point, and frequency f = 1/T counts cycles per second.
= λ/T = fλ
Use λ in metres and f in Hz to obtain v in m/s. A metre per cycle multiplied by cycles per second gives metres per second.
Estimate the speed scale
Assume roughly 1 m between corresponding crests and about 5 cycles each second. The propagation speed is then of order 5 m/s. These rough inputs check the scale before using the exact supplied wave values.
Worked mechanical waves
Keep metres and seconds consistent
For the transverse model with λ = 0.80 m and T = 0.20 s:
v = 5.0 × 0.80 = 4.0 m/s
This agrees with a crest advancing 0.20 m in 0.050 s. It does not mean a string particle travels right at 4.0 m/s. That particle oscillates transversely, with a changing local velocity.
For the separate longitudinal model, λ = 0.60 m and T = 2.0 ms = 0.0020 s:
v = 500 × 0.60 = 300 m/s
The 300 m/s is the propagation speed of its pattern, not a constant speed of its material particles. At a displacement extreme, a sinusoidally oscillating particle can be momentarily at rest while the wave continues to progress.
Try it step by step
Work it out in steps: Wavelength = v / f in m, then Separation as a fraction of a wavelength, then Phase difference in degrees.
Show the answer
Problem 1.
Wavelength = v / f in m: wavelength = 340 / 500 = 0.68 m
Separation as a fraction of a wavelength: 0.17 / 0.68 = 0.25 of a wavelength
Phase difference in degrees: Phase difference = 0.25 x 360 = 90 degrees
Problem 2.
Wavelength = v / f in m: wavelength = 340 / 250 = 1.36 m
Separation as a fraction of a wavelength: 0.68 / 1.36 = 0.50 of a wavelength
Phase difference in degrees: Phase difference = 0.50 x 360 = 180 degrees (antiphase)
Problem 3.
Wavelength = v / f in m: wavelength = 340 / 1000 = 0.34 m
Separation as a fraction of a wavelength: 0.085 / 0.34 = 0.25 of a wavelength
Phase difference in degrees: Phase difference = 0.25 x 360 = 90 degrees
Use c for electromagnetic waves in vacuum
The symbol c denotes the speed of electromagnetic waves in a vacuum, with SI unit m/s. For vacuum propagation, v = c and c = fλ.
Worked vacuum wavelength
Use supplied c = 3.00 × 108 m/s and light frequency f = 6.00 × 1014 Hz:
= (3.00 × 108)/(6.00 × 1014)
= 5.00 × 10-7 m = 500 nm
One nanometre is 10-9 m. In a material medium, use the appropriate propagation speed rather than automatically substituting the vacuum value c.
Changing the source frequency does not necessarily change propagation speed. In the same unchanged medium under a nondispersive approximation, speed stays fixed and wavelength adjusts according to λ = v/f. This condition matters: propagation speed can depend on frequency in other media or frequency ranges.
When obtaining v from data, keep wavelength and frequency from the same wave and medium. A spatial image provides λ; a fixed-point time record provides T or f. Read their scales and references before combining them.