Wave speed, frequency, and wavelength are linked by fλ = c

Evidence

The all-important relation fλ = c, where f is the frequency, λ is the wavelength, and c is the speed of the wave, can always be used to determine the third variable if two others are known. Now we know the frequency fn of the modes, and the wavelength λn is determined from equation 8.10: nπ λn/L = 2π, or λn = 2L/n, n = 1, 2, … . Then, from equation 8.8 and fλ = c, we have We have found that the speed of waves on the string is given in terms of the tension and the mass density as c = (T/ρ)1/2, independent of the mode number, and therefore is independent of the wavelength and frequency, just as with sound in air. — Eric J. Heller, Why You Hear What You Hear- An…, 822

Categorization

• DEFINE: Introduces the wave relation fλ = c and derives mode wavelengths λn = 2L/n.