ACT Science: Wave Speed, Frequency, Wavelength—v=fλ Explained

Wave speed (v) is the distance a wave travels per unit time. Frequency (f) is the number of waves per second (measured in Hz). Wavelength (λ) is the distance between consecutive wave peaks. The equation v=fλ shows that wave speed is the product of frequency and wavelength. For light and sound, increasing frequency decreases wavelength (if speed is constant). This single equation connects three fundamental wave properties and appears in nearly every ACT Science physics passage about waves, light, or sound.

Example: A sound wave has frequency 500 Hz and travels at 340 m/s (speed of sound). Wavelength λ=v/f=340/500=0.68 m.

Calculation 1 (Find wavelength): A radio wave has frequency 100 MHz (10⁸ Hz) and travels at 3×10⁸ m/s. λ=v/f=(3×10⁸)/(10⁸)=3 m. Calculation 2 (Find frequency): A wave on a string has wavelength 0.5 m and travels at 20 m/s. f=v/λ=20/0.5=40 Hz. Calculation 3 (Find speed): A light wave has frequency 5×10¹⁴ Hz and wavelength 6×10⁻⁷ m. v=fλ=(5×10¹⁴)(6×10⁻⁷)=3×10⁸ m/s (speed of light). Know the three rearranged forms: f=v/λ, λ=v/f, v=fλ.

Practice these daily until you solve each in under 1 minute.

Scenario 1: A sound wave has frequency 1000 Hz and wavelength 0.34 m. Find speed. v=fλ=(1000)(0.34)=340 m/s. Scenario 2: Light has wavelength 400 nm (4×10⁻⁷ m). Speed of light is 3×10⁸ m/s. Find frequency. f=v/λ=(3×10⁸)/(4×10⁻⁷)=7.5×10¹⁴ Hz. Scenario 3: A wave on a string has speed 15 m/s. If frequency doubles, what happens to wavelength? If f doubles and v is constant, then λ=v/f halves. Do these three scenarios daily until conceptual understanding is automatic.

Remember: frequency and wavelength are inversely related (if one increases, the other decreases, assuming constant speed).

Wave property questions appear in 1-2 ACT Science passages. They are computational; once you know v=fλ and can rearrange it, solving is mechanical. Investing 15 minutes in this equation yields 1-2 guaranteed points because the concept is simple and formulas are provided or easy to recall.

Master wave equations one day before the test. On test day, you will answer wave questions confidently.