Physics · WPH12 (Unit 2)

The wave equation and resistivity

Unit 2 covers waves and electricity. Two equations you will use constantly are v = fλ and R = ρL/A.

Wave equation

Wave speed v = frequency f x wavelength λ. Frequency is in Hz, wavelength in m, speed in m/s. Period T = 1/f.

Resistivity

The resistance of a uniform wire is R = ρL / A, where ρ is the resistivity of the material (Ω m), L the length and A the cross-sectional area. Doubling the length doubles R; doubling the area halves R.

Ohm's law reminder

V = IR. Power P = IV = I2 R = V2 / R.

Worked example

A sound wave has frequency 500 Hz and wavelength 0.68 m. Find its speed.

  1. v = fλ = 500 x 0.68

Answer: v = 340 m/s

Key idea: v = fλ, T = 1/f. R = ρL/A. V = IR.

Check yourself

  1. A wave has f = 50 Hz and λ = 4.0 m. Find v.
    Show answer

    200 m/s. v = fλ = 200 m/s.

  2. Light of speed 3.0 x 108 m/s has frequency 6.0 x 1014 Hz. Find λ in nm.
    Show answer

    500 nm. λ = v/f = 5.0 x 10-7 m = 500 nm.

  3. Find the period of a wave of frequency 20 Hz.
    Show answer

    0.05 s. T = 1/f = 0.05 s.

  4. A wire's length is doubled and its area is unchanged. Its resistance
    • doubles
    • halves
    • stays the same
    • quadruples
    Show answer

    doubles. R = ρL/A, so R is proportional to L.

  5. A wire has ρ = 5.0 x 10-7 Ω m, L = 2.0 m and A = 1.0 x 10-6 m2. Find R.
    Show answer

    1 Ω. R = ρL/A = (5.0 x 10-7 x 2.0) / (1.0 x 10-6) = 1.0 Ω.

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Sources

Last updated 7 November 2026. Spotted a mistake? Email alevel@lifereadysociety.com.