【Physics】Wave Motion: Master the Basics of Waves!
Hello everyone! Welcome to the "Wave Motion" section of physics.
When you hear the word "wave," you might think of ocean waves. But in reality, our world is filled with waves! The "light" you are using to read this text, and the "sound" you hear, are all types of waves.
It might feel difficult at first due to all the new terms and formulas, but don't worry. Let's take it one step at a time while focusing on visualizing the concepts!
1. The Basics of Waves: What is a Wave?
A wave is a phenomenon where a vibration (oscillation) occurring at one point is transmitted to its neighbors one after another. There is one super important point here!
Key Point: When a wave propagates, the "medium" (the material transmitting the wave) only oscillates in place; it does not travel. Only the "energy" moves!
Example: A stadium wave. The spectators (the medium) only move up and down, they don't change their seats, right? But the "wave" travels all the way around the stadium.
Wave Terminology (Make sure to learn these!)
- Wavelength (\(\lambda\)) [m]: The length of one full wave cycle (from crest to the next crest).
- Amplitude (\(A\)) [m]: The height of the crest (the maximum displacement from the center).
- Period (\(T\)) [s]: The time it takes for the wave to oscillate once.
- Frequency (\(f\)) [Hz]: The number of oscillations the wave completes in one second.
- Wave Speed (\(v\)) [m/s]: The distance the wave travels in one second.
★ Super Important Formula: The Universal Wave Equation
This is the most essential formula in wave physics!
\(v = f\lambda\)
(Speed = Frequency per second × Length of one wave)
Also, since the relationship between period and frequency is \(f = \frac{1}{T}\), it can also be written as \(v = \frac{\lambda}{T}\).
Study Tip: Think of it the same way as "Speed = Distance ÷ Time." If you think of it as "Wave Speed = Wavelength ÷ Period," you'll remember it naturally!
[Summary]
Waves transport "energy," not the "medium." You must memorize \(v = f\lambda\)!
2. Transverse Waves and Longitudinal Waves
There are two types of waves based on their direction of oscillation. This is a common point of confusion!
① Transverse Waves
Waves that oscillate perpendicular to the direction in which the wave travels.
Example: Light, waves created by shaking a rope.
Since they look like they are "undulating," they are easy to visualize.
② Longitudinal Waves
Waves that oscillate parallel (in the same direction) to the direction in which the wave travels.
Example: Sound waves, waves created by pushing and pulling a spring.
These are also called "compressional waves" because they transmit areas where the air is dense (compression) and thin (rarefaction).
Common Misconception: People often think, "Longitudinal waves can't be graphed," but for convenience, we rotate the oscillation of a longitudinal wave by 90 degrees to represent it as a transverse wave graph (a y-x graph). This is called the "transverse representation of a longitudinal wave."
[Summary]
Transverse waves oscillate "perpendicularly," and longitudinal waves oscillate "parallelly"! Remember that sound is a "longitudinal wave."
3. Wave Properties: What Happens When They Overlap?
Waves display curious properties when they collide with other waves.
Principle of Superposition
When two waves meet, the height at that location is the "sum of the heights of each individual wave." After they pass through each other, they continue on in their original forms as if nothing happened (Independence of Waves).
Standing Waves
When two waves of the same shape and speed traveling in opposite directions overlap, they create a large wave that appears to stand still. This is a standing wave.
- Node: Points that do not vibrate at all.
- Antinode: Points that vibrate with maximum amplitude.
Trivia: Standing waves are actually what happens inside a microwave oven! The reason food heats unevenly is because of the "antinodes (strong)" and "nodes (weak)" of the waves. That’s why the plate inside rotates.
[Summary]
When waves overlap, they add up. When waves traveling in opposite directions overlap, they create a "standing wave"!
4. Properties of Sound: What is the Doppler Effect?
Since sound is a type of wave, the rules we learned apply here as well. The Doppler effect is especially common on exams.
Doppler Effect
This is the phenomenon where a siren sounds higher-pitched as an ambulance approaches and lower-pitched as it moves away.
- When approaching: The waves are compressed, so the wavelength becomes shorter, and the frequency \(f\) increases (pitch gets higher).
- When moving away: The waves are stretched out, so the wavelength becomes longer, and the frequency \(f\) decreases (pitch gets lower).
Formula Tip: \(f' = f \times \frac{V - v_o}{V - v_s}\)
(\(V\): speed of sound, \(v_o\): velocity of the observer, \(v_s\): velocity of the sound source)
*Rather than rote memorizing the formula at first, it is more important to have a strong mental image that "approaching makes the sound higher!"
[Summary]
Sound pitch is determined by "frequency." The Doppler effect is caused by "changes in wavelength"!
5. Properties of Light: Reflection and Refraction
Finally, let's touch briefly on light. When light enters a different medium (like from air into water), it bends. This is refraction.
Law of Refraction (Snell's Law)
\(\frac{\sin \theta_1}{\sin \theta_2} = \frac{v_1}{v_2} = \frac{\lambda_1}{\lambda_2} = n_{12}\)
It looks like a difficult formula, but the point is simple:
"When light enters a medium where its speed decreases, the angle also decreases, and the wavelength shortens."
Example: The bottom of a swimming pool looks shallow because when light enters the water, it refracts, changing the angle at which it reaches our eyes.
[Summary]
When light travels to a new medium, "speed, wavelength, and angle" change as a set!
Final Words: Mastering Physics Waves
At first, you might be confused by the difference between "y-x graphs" and "y-t graphs":
- y-x graph: A "photograph" at a single moment in time (the shape of the whole wave).
- y-t graph: A "video" of a specific location (the passage of time at one point).
It might feel tough at first, but you'll be fine. Start by learning how to perform calculations using \(v = f\lambda\). As you solve more problems, the movement of waves will start to play like an animation in your head! Good luck!