What is the wave equation and how is it used?

The wave equation is $v = f\lambda$, linking wave speed, frequency and wavelength, and it is printed on the Reference Tables along with $T = 1/f$. Any one of the three quantities can be found from the other two by rearranging. In a given medium the wave speed is fixed, so frequency and wavelength are inversely related. For electromagnetic waves in a vacuum the speed is the speed of light, $c = 3.00 \times 10^8$ m/s.

Why does the pitch of a passing siren change?

This is the Doppler effect: the apparent frequency changes because of relative motion between the source and the observer. As the source approaches, the waves bunch up and the pitch heard is higher than the actual pitch; as it recedes, the waves spread out and the pitch is lower. The source's true frequency never changes; only the frequency received changes. There is no Doppler equation on the Reference Tables, so it is assessed qualitatively.

What is the difference between diffraction and interference?

Diffraction is the spreading of a single wave around an obstacle or through a gap, most noticeable when the gap is about the size of the wavelength. Interference is the combining of two overlapping waves by superposition: constructive (in phase, larger amplitude) where crest meets crest, destructive (out of phase, smaller amplitude) where crest meets trough. Standing waves are an interference pattern with fixed nodes and antinodes. Both behaviors are evidence that light is a wave.

How is the electromagnetic spectrum ordered?

By increasing frequency (and decreasing wavelength): radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, gamma rays. Within visible light, red has the lowest frequency and violet the highest. All electromagnetic waves are transverse and travel at the speed of light in a vacuum, needing no medium. A higher frequency means a shorter wavelength and more energy per photon, which is why gamma rays are more damaging than radio waves.

New YorkPhysics

Regents Physics waves: a complete skills guide to wave properties, the wave equation, sound, the Doppler effect, reflection, refraction, diffraction, interference and the electromagnetic spectrum

Q: How do I handle reflection and refraction problems?

Measure all angles from the normal. For reflection, the angle of incidence equals the angle of reflection. For refraction, use the index of refraction $n = c/v$ and Snell's law $n_1\sin\theta_1 = n_2\sin\theta_2$. Light bends toward the normal entering a denser (higher-$n$) medium and away from the normal entering a less dense one. The frequency is unchanged; the speed and wavelength change together. All three equations are on the Reference Tables.

A deep-dive Regents Physics skills guide to the waves module: wave properties and the wave equation, sound and the Doppler effect, reflection and refraction with Snell's law, diffraction and interference, and the electromagnetic spectrum. Includes worked examples and the constructed-response technique Regents markers reward.

Generated by Claude Opus 4.817 min readPS-PHYS 4.3Updated 2026-06-02

Reviewed by: AI editorial process; not yet individually human-reviewed

Jump to a section

Why the waves module rewards clear definitions
Wave properties and the wave equation
Sound and the Doppler effect
Reflection and refraction
Diffraction, interference and the electromagnetic spectrum
Check your knowledge

Why the waves module rewards clear definitions

The waves strand mixes reliable calculations (the wave equation, the index of refraction, Snell's law) with conceptual questions (the Doppler effect, diffraction, interference, the spectrum). Most marks come from precise definitions and from measuring angles correctly. This guide ties together the dot-point pages, each with its own practice: wave properties and the wave equation, sound and the Doppler effect, reflection and refraction, diffraction and interference and the electromagnetic spectrum.

Wave properties and the wave equation

A wave transfers energy without matter. Its amplitude (linked to energy), wavelength $\lambda$ (a distance), frequency $f$ (waves per second, Hz) and period $T$ (time per wave, with $T = 1/f$ ) describe it fully. Waves are transverse (medium vibrates perpendicular to travel: light, water) or longitudinal (medium vibrates parallel: sound). The wave equation $v = f\lambda$ links speed, frequency and wavelength; in a given medium the speed is fixed, so higher frequency means shorter wavelength. Both $v = f\lambda$ and $T = 1/f$ are on the Reference Tables.

Sound and the Doppler effect

Sound is a longitudinal mechanical wave needing a medium, so it cannot travel through a vacuum. Its pitch depends on frequency, its loudness on amplitude. The Doppler effect is the apparent change in frequency from relative motion: approaching source means higher pitch, receding source means lower pitch, with the true frequency unchanged. The same effect shifts the light of receding stars toward the red. There is no Doppler formula on the tables.

Reflection and refraction

Measure all angles from the normal. Reflection: angle of incidence equals angle of reflection. Refraction: light bends when its speed changes between media. The index of refraction is $n = \dfrac{c}{v}$ (at least 1, dimensionless), and Snell's law is $n_1\sin\theta_1 = n_2\sin\theta_2$ . Light bends toward the normal entering a denser medium and away entering a less dense one; frequency stays the same while speed and wavelength change. These three equations are on the tables (the thin-lens equation is not, so optics is done with ray diagrams).

Diffraction, interference and the electromagnetic spectrum

Diffraction is the spreading of a wave around an obstacle or through a gap, greatest when the gap is near the wavelength. Interference combines overlapping waves by superposition: constructive in phase (larger amplitude), destructive out of phase (smaller). Standing waves have fixed nodes (no motion) and antinodes (maximum motion). Interference and diffraction of light prove its wave nature. The electromagnetic spectrum, in order of increasing frequency, is radio, microwave, infrared, visible, ultraviolet, X-ray, gamma; all are transverse and travel at $c = 3.00 \times 10^8$ m/s in a vacuum, with $c = f\lambda$ .

A refraction calculation with the wave equation

Light of frequency $5.0 \times 10^{14}$ Hz travels from air into a glass of index $1.5$ . (a) Find its speed in the glass. (b) Find its wavelength in the glass. Take $c = 3.00 \times 10^8$ m/s.

step 1 Find the speed in the glass

From $n = \dfrac{c}{v}$ , $v = \dfrac{c}{n} = \dfrac{3.00 \times 10^8}{1.5} = 2.0 \times 10^8$ m/s.

step 2 Note the frequency is unchanged

The frequency stays $5.0 \times 10^{14}$ Hz on entering the glass (it is set by the source).

step 3 Find the wavelength in the glass

$\lambda = \dfrac{v}{f} = \dfrac{2.0 \times 10^8}{5.0 \times 10^{14}} = 4.0 \times 10^{-7}$ m.

step 4 Interpret

In the glass the light is slower ( $2.0 \times 10^8$ m/s) and its wavelength shorter ( $4.0 \times 10^{-7}$ m), while the frequency is unchanged, consistent with $v = f\lambda$ .

The waves module rests on the wave equation $v = f\lambda$ (with $T = 1/f$ ). Waves are transverse or longitudinal; sound is longitudinal and needs a medium, so the Doppler effect (approaching higher, receding lower) changes only the received frequency. Reflection has equal angles from the normal; refraction uses $n = c/v$ and Snell's law $n_1\sin\theta_1 = n_2\sin\theta_2$ , with light bending toward the normal in a denser medium and frequency unchanged. Diffraction is wave spreading (greatest near the wavelength); interference combines waves by superposition (constructive in phase, destructive out of phase), with standing waves having nodes and antinodes. The electromagnetic spectrum (radio to gamma, increasing frequency) is all transverse waves at $c$ in a vacuum, using $c = f\lambda$ . Measure all optics angles from the normal.

Check your knowledge

A mix of recall, calculation and reasoning questions covering the waves module. Attempt them under timed conditions, then check against the solutions.

State the difference between a transverse and a longitudinal wave. (2 marks)
A wave has frequency $6.0$ Hz and wavelength $0.50$ m. Calculate its speed. (2 marks)
State why sound cannot travel through a vacuum. (1 mark)
State what happens to the pitch an observer hears as a sound source approaches. (1 mark)
State the law of reflection. (1 mark)
Light travels at $2.0 \times 10^8$ m/s in a medium. Calculate the index of refraction ( $c = 3.00 \times 10^8$ m/s). (2 marks)
Light passes from air into water (higher $n$ ). State whether it bends toward or away from the normal. (1 mark)
State what happens to the amplitude when two waves interfere destructively. (1 mark)
State the order of the electromagnetic spectrum by increasing frequency. (2 marks)
A radio wave has frequency $5.0 \times 10^7$ Hz. Calculate its wavelength in a vacuum ( $c = 3.00 \times 10^8$ m/s). (2 marks)

Solutions

Q1: Transverse: the medium vibrates perpendicular to the wave direction. Longitudinal: the medium vibrates parallel to the wave direction.
Q2: $v = f\lambda = (6.0)(0.50) = 3.0$ m/s.
Q3: Sound is a mechanical wave that needs particles of a medium to vibrate; a vacuum has none.
Q4: The pitch heard is higher than the actual pitch (the waves bunch up, raising the apparent frequency).
Q5: The angle of incidence equals the angle of reflection, both measured from the normal.
Q6: $n = \dfrac{c}{v} = \dfrac{3.00 \times 10^8}{2.0 \times 10^8} = 1.5$ .
Q7: Toward the normal (it enters a denser, higher-index medium and slows down).
Q8: The amplitude decreases (the displacements partly or fully cancel because the waves are out of phase).
Q9: Radio, microwave, infrared, visible light, ultraviolet, X-ray, gamma (increasing frequency).
Q10: $\lambda = \dfrac{c}{f} = \dfrac{3.00 \times 10^8}{5.0 \times 10^7} = 6.0$ m.

Sources & how we know this

Reference Tables for Physical Setting/Physics — NYSED (2006)
Physical Setting/Physics Regents examinations — NYSED (2019)