Module 05: Waves and Optics · quiz worth 20 pts
The names are easier when each one has a different physical question.
Reflection returns; refraction transmits into a new speed and may bend.
Diffraction spreads the wave, strongest when the opening is comparable to wavelength.
Interference adds signed displacements; beats are the time-varying loudness from nearby frequencies.
Optional interactive: PhET Waves Intro lets you compare reflection and interference in water, sound, and light models. Use it to test a prediction, not as evidence for an assigned response.
Physics Classroom: The Doppler Effect — Optional visual explanation of wavefront spacing and observed frequency. Keep pitch separate from changes in loudness.
Got it now? Scroll back up and re-read the section — it should land differently.
When a wave hits a boundary and bounces back, that's reflection. Angles are always measured from the normal, an imaginary line perpendicular to the surface, not from the surface itself. The law of reflection: the angle of incidence equals the angle of reflection.
A ray traveling exactly along the normal (angle of incidence 0°) reflects straight back the way it came.
Refraction happens when a wave crosses into a medium where its speed is different, like light passing from air into water. That speed change bends the wave's path, which is why a pencil in a glass of water looks broken at the surface. If the wave slows down entering the new medium, it bends toward the normal; if it speeds up, it bends away from the normal. A ray traveling along the normal doesn't bend at all, just slows down or speeds up in place.
Here is the one thing worth locking in before 05.07: the wave's frequency never changes when it crosses a boundary. The source is still producing the same number of waves per second, so f stays fixed. What changes is wavelength and speed together, since v = fλ: if v drops and f is fixed, λ must shrink to match.
A wave hitting a boundary rarely does only one of these. Some of its energy reflects back into the first medium, and the rest transmits into the second medium and refracts. How much goes each way depends on the angle and the two materials' properties.
Notice the refracted ray bends toward the normal (a smaller angle than the incident ray), because it's entering the slower medium. The reflected ray keeps the incident ray's full angle, on the other side of the normal.
Diffraction is the bending of a wave around an obstacle or through an opening. It's strongest when the wavelength is close to or larger than the size of the opening or obstacle. That's why you can hear someone talking around a corner (sound wavelengths are on the order of a meter, comparable to a doorway) but can't see around that same corner (light's wavelength is under a millionth of a meter, far too small to diffract noticeably at that scale).
When two waves overlap in the same medium, they combine by the principle of superposition: at every point, add the two waves' displacements, keeping track of sign. Two crests meeting produce a bigger crest, twice the amplitude if they match exactly; that's constructive interference. A crest meeting a trough of equal size cancels to zero amplitude; that's destructive interference. Either way, the waves pass through each other unchanged and keep going, exactly as they were before they overlapped.
When two waves of slightly different frequency overlap at the same location, they drift in and out of sync over time: constructive interference (loud) at one moment, destructive interference (quiet) a fraction of a second later, repeating. That pulsing loudness is called beats. Play a 440 Hz tone and a 441 Hz tone together and you'll hear one throb per second.
f_beat, f₁, and f₂ all in hertz. The beat frequency is how many loud-soft pulses you hear each second.
This is the one correction worth flagging directly: beats are a pulsing loudness over time at one location. A standing wave is a fixed pattern in space, made by two waves of the same frequency traveling in opposite directions, most commonly a wave reflecting off a fixed end and overlapping the wave still arriving. Certain points, called nodes, never move at all. Halfway between them, antinodes vibrate with maximum amplitude. Unlike a traveling wave, the pattern doesn't move left or right, it just oscillates in place, which is why a plucked guitar string looks like it has fixed dead spots along its length.
When a sound source moves toward or away from you, you hear a pitch shift, higher approaching, lower receding, called the Doppler effect. Keep it separate from the ordinary volume change caused by distance: as any source gets closer its sound simply gets louder, regardless of whether it's moving. Both effects happen at once with a passing ambulance; only the pitch change is the Doppler effect.
The wave source keeps emitting at its own fixed frequency, but because the source is moving, the waves it emits going in the direction of travel get compressed closer together, and the ones emitted behind it get stretched farther apart. A closer wave spacing (shorter wavelength) means a listener ahead of the source hears more wave crests arrive each second, a higher frequency, even though the source's own emission frequency never changed.
The source lesson keeps this qualitative (which direction the pitch shifts), and its own practice questions never require a formula, so that's the level to be solid at for this course. For completeness, the exact relationship is f_observed = f_source × v / (v ∓ v_source), where v is the speed of sound and the sign depends on whether the source approaches (−, pitch rises) or recedes (+, pitch falls); you will not be asked to calculate with it in this course.
Ask whether the observation is about frequency or intensity.
Relative motion changes wavefront spacing, so approaching sounds higher and receding sounds lower.
Distance changes how much wave energy reaches you. That can happen even when the source is not moving.
Got it now? Scroll back up and re-read the section — it should land differently.
v in m/s, λ in m, f in Hz (waves/second — "wave" itself is not a unit).
Useful for round-trip/echo problems: d is the total distance traveled, so an echo's d is twice the one-way depth.
Find the time between the transducer sending the pulse and detecting the echo.
t ≈ 3.66 × 10⁻⁴ s. Forgetting to double the distance is the single most common mistake on echo problems.
Find the wavelength, which sets the smallest observable detail.
λ = 7.5 × 10⁻⁵ m. A higher ultrasound frequency gives a shorter wavelength and finer detail, which is why different scans use different frequencies.
It doesn't. Only wavelength and speed change when a wave crosses into a new medium; the source's emission rate (frequency) is what it always was.
The source material's own wording does this. Beats are a loudness pulsing over time from two close but different frequencies. A standing wave is a fixed spatial pattern of nodes and antinodes from two equal frequencies traveling in opposite directions.
A source just getting closer sounds louder whether or not it's moving. The Doppler effect is specifically the pitch (frequency) shift caused by the source's motion, not the loudness change.
Sonar, ultrasound, and radar problems ask for a distance the wave travels once, but the wave actually travels there and back. Double the one-way distance before using v = d/t.
Frequency in v = λf is waves per second, but the unit that survives the calculation is just 1/s, or Hz. "Wave" is a count, not a unit.
These mirror the source lesson's own practice set: wave-speed calculations, a beat-frequency problem, and both directions of the Doppler car-horn question.
Tick these off as you go. Saved in this browser.
