【Physics】Welcome to the World of Waves!
Hello everyone! Do you feel like "Physics waves are invisible and full of complicated formulas, so they're impossible to understand"? Don't worry! Waves are essentially the "sound" and "light" we experience in our everyday lives. In this chapter, we will organize how waves propagate and what properties they have, keeping a strong focus on visualizing the concepts.
Let's master the key points often tested in the Common Test and turn this section into a source of easy points!
1. Basics of Waves: Understanding What a Wave Is
A wave is a phenomenon where a vibration generated at one point is transmitted to neighboring points one after another. A super important point here is that "when a wave propagates, the medium (air, water, etc.) only moves back and forth in place; it does not travel with the wave!"
4 Key Terms for Waves
First, let's master these four terms, which are essential for calculation problems.
1. Amplitude \(A\) [m]: The height of the crest (or depth of the trough).
2. Wavelength \(\lambda\) [m]: The length from one crest to the next.
3. Period \(T\) [s]: The time it takes for one full wave to pass a point.
4. Frequency \(f\) [Hz]: How many waves pass by in one second.
★ Remember this! The Ultimate Formula
The formula for wave speed \(v\) is used more than any other in wave physics.
\(v = f\lambda\) (Speed = Number per second × Length of one wave)
Also, the relationship between period and frequency is \(f = \frac{1}{T}\). Combining these, we can also write:
\(v = \frac{\lambda}{T}\)
Tip: Pay attention to the units. [m/s] = [Hz] × [m]. If you ever forget the formula, you can derive it from the units!
Transverse and Longitudinal Waves
There are two main types of waves:
・Transverse wave: The direction of vibration is "perpendicular" to the direction the wave travels. Ex: Light, vibrating strings.
・Longitudinal wave: The direction of vibration is "parallel" to the direction the wave travels. Ex: Sound. Also known as "compression waves."
*Since longitudinal waves are difficult to graph as-is, we represent them by shifting the displacement to the right upward and to the left downward to make them look like "transverse waves." This is called "transverse wave representation of longitudinal waves!"
【Key Takeaway】
Definitely memorize the basic formula \(v = f\lambda\)! Try to visualize the differences between wave types (longitudinal vs. transverse).
2. Wave Graphs: The Essence of y-x and y-t Graphs
Many students get confused by these graphs. However, the logic is very simple!
y-x Graph (A Snapshot)
Think of this as a "photograph" taken with a camera. Since the horizontal axis is position \(x\), you can see the actual shape of the wave. You use this to read the "wavelength \(\lambda\)".
y-t Graph (A Video)
This is a "recording" of just one specific point over time. Since the horizontal axis is time \(t\), you use this to read the "period \(T\)".
Common Mistake: Many students assume every graph shows wavelength without checking the horizontal axis. If the axis is \(x\), it’s wavelength; if it's \(t\), it’s period. Say this three times before your test!
Pro Tip: When solving problems where the wave moves, try drawing the wave after a short period of time using a "dashed line." This makes it easy to see whether the medium at each point is moving "up" or "down"!
3. Properties of Waves: Reflection, Refraction, and Interference
These are the rules for when waves hit a wall or move into a different medium.
Reflection Rules
・Free-end reflection: The end is free to move. The wave reflects with the "same" shape.
・Fixed-end reflection: The end is firmly fixed. The wave reflects "upside down" (a phase shift of \(\pi\)).
Law of Refraction (Snell's Law)
When a wave enters a different material, it bends because its speed changes.
\(\frac{\sin \theta_1}{\sin \theta_2} = \frac{v_1}{v_2} = \frac{\lambda_1}{\lambda_2} = n_{12}\)
*\(n_{12}\) is the refractive index. Important note! The "frequency \(f\)" never changes, even if the medium changes! This is a frequent target for the Common Test.
Standing Waves (Stationary Waves)
When a wave traveling right and a wave traveling left overlap, they create a "non-traveling wave" that appears to flap in place. This is a standing wave.
・Antinode: The point that vibrates most violently.
・Node: The point that doesn't move at all.
Tip: The distance between adjacent nodes is half the wavelength (\(\frac{\lambda}{2}\)) of the original wave!
【Key Takeaway】
Frequency \(f\) is invariant during refraction! The distance between standing wave nodes is \(\frac{\lambda}{2}\)!
4. Sound Properties and the Doppler Effect
Sound is a type of wave (longitudinal wave). The "Doppler effect" is the main challenge here.
Doppler Effect: Why does the pitch change?
You know how an ambulance siren sounds higher as it approaches and lower as it drives away? The formula looks scary, but it's not if you think about it this way:
\(f' = f \times \frac{V \pm v_o}{V \mp v_s}\)
(\(V\): speed of sound, \(v_o\): observer speed, \(v_s\): source speed)
★ Tips for memorizing the formula
Think: "When approaching, if the denominator gets smaller or the numerator gets bigger, \(f'\) becomes larger (higher pitch)." If the source is approaching, make the denominator minus; if the observer is approaching, make the numerator plus. Don't overthink it—the best way to avoid mistakes is to "choose the signs that make the frequency go higher as they approach!"
Beats
When two sounds with slightly different frequencies are played at the same time, you hear a "wobbling" sound (wah-wah-wah). The number of beats per second \(n\) is a simple subtraction:
\(n = |f_1 - f_2|\)
【Key Takeaway】
For the Doppler effect, construct the formula so that "approaching = higher pitch"! Beats are just simple subtraction!
5. Light Properties: Reflection, Refraction, and Interference
Finally, "light." Light is a wave, but it also has particle properties; here, we focus on its "wave" nature.
Light Refraction and Total Internal Reflection
When light travels from water to air, if the angle exceeds a certain limit (critical angle), the light cannot exit and is completely reflected. This is total internal reflection. It is used in things like fiber optics.
Light Interference (Young's Experiment, Diffraction Grating)
This is the phenomenon where light overlaps to create bright and dark spots. For the Common Test, the "path difference" is crucial.
・Path difference is an integer multiple of the wavelength (\(m\lambda\)) \(\rightarrow\) Constructive interference (bright)
・Path difference is an integer plus a half (\((m+1/2)\lambda\)) \(\rightarrow\) Destructive interference (dark)
*Watch out: If there is a phase shift due to reflection (like fixed-end reflection), these conditions are reversed!
It might feel difficult at first, but you'll be fine. If you think of light interference as simply calculating "which path is longer and by how much?", it becomes like solving a puzzle.
【Key Takeaway】
For light interference, check how many wavelengths the "path difference" is! Be careful of reversals caused by reflection!
Great job finishing your study on waves!
Wave physics becomes much easier once you combine "memorizing formulas" + "drawing diagrams to visualize." Start by mastering the basic \(v = f\lambda\). I'm rooting for you!