Wave Properties & the Wave Equation

You’ll be able to

Distinguish transverse from longitudinal waves and define wave quantities
Relate wave speed, frequency, and wavelength through v = fλ
Predict how wavelength changes when frequency changes at constant speed

What a wave carries

A wave is a disturbance that transfers energy through a medium (or space) without transporting matter — the water bobs up and down while the wave rolls onward. In a transverse wave the medium moves perpendicular to the wave’s travel (light, waves on a string); in a longitudinal wave it moves parallel, as compressions and rarefactions (sound). The key measurements are wavelength (λ), the length of one full cycle; frequency (f), cycles per second in hertz; period (T = 1/f), the time for one cycle; and amplitude, the size of the disturbance, which sets the energy.

The wave relationship

v = f · λ · f = 1 / T

Wave speed equals frequency times wavelength. In a given medium the speed is fixed by the medium’s properties, so frequency and wavelength trade off inversely.

Speed belongs to the medium

A wave’s speed is set by the medium, not by how it was made. Once v is fixed, the relationship v = fλ means frequency and wavelength are inversely linked: raise the frequency and the wavelength must shrink to keep v constant. This is why a high-pitched sound (high f) has a short wavelength while a deep bass note (low f) has a long one, both traveling at the same speed through the same air. Frequency is set by the source; the medium then determines the wavelength.

Worked example

A wave has a frequency of 50 Hz and a wavelength of 4.0 m. What is its speed?

1.Use the wave relationship v = fλ.
2.Substitute: v = (50 Hz)(4.0 m).
3.Multiply: 50 × 4.0 = 200.

Answer: v = 200 m·s⁻¹.

Checkpoint

A wave has a frequency of 50 Hz and a wavelength of 4.0 m. What is its speed?

Tip

Amplitude and frequency are independent. Amplitude sets a wave’s energy (loudness for sound, brightness for light); frequency sets its pitch or color. Changing one does not change the other.

Checkpoint

A wave’s frequency doubles while its speed stays constant (same medium). What happens to its wavelength?

On the exam

When a wave passes from one medium to another, its frequency stays the same (set by the source), while its speed and wavelength both change. This fact underlies refraction: light slows in glass, so its wavelength shortens while its color (frequency) is unchanged.

Answer the 2 checkpoints as you read.