【Physics Basics】Mastering the Fundamentals of Waves!
Hello everyone! Let's start our journey into the world of "Waves."
Many people might feel that "Physics waves look difficult with all those formulas..." But in reality, our world is overflowing with waves. Voices, music, radio waves for smartphones, and the rhythm of the ocean—all of these share the properties of waves. In this chapter, we will break down the nature and rules of waves step-by-step using familiar examples. It might feel a bit strange at first, but once you grasp the rules, it becomes as fun as solving a puzzle. Let's do our best together!
1. What is a Wave, Really?
A wave is a phenomenon where a vibration generated at one location is transmitted successively to its surroundings.
● Organizing Important Terminology
Wave Source: The location where the vibration begins.
Medium: The material through which a wave travels (e.g., water, air, a string).
Wave: The phenomenon of the vibration being transmitted itself.
● Key Point! The Medium "Does Not Move"
Think about the "stadium wave" performed by spectators. The wave travels around the stadium, but each spectator simply stands up and sits down in their own seat, right? They don't move to the next seat over.
Physics waves are the same. The medium only vibrates in place and does not move along with the wave. The only thing that travels is the "energy of the vibration."
【Common Mistake】
People sometimes think, "When a sound wave travels, air particles fly from the speaker to the listener's ear." This is incorrect. Air particles only vibrate in place, bumping into each other to pass on the shape of the vibration.
Summary: Waves transmit a "state" or "condition," not the medium itself!
2. Graphs and Formulas Representing Waves
To describe the properties of waves, we use several "numbers." This is the first step toward solving calculation problems.
● Anatomy of a Wave
Crest: The highest point of a wave.
Trough: The lowest point of a wave.
● 5 Important Keywords for Waves
1. Amplitude \(A\): The extent of the vibration. The height from the center to a "crest." The unit is meters \([m]\).
2. Wavelength \(\lambda\): The distance from one crest to the next. The unit is meters \([m]\).
3. Period \(T\): The time taken for one full vibration. The unit is seconds \([s]\).
4. Frequency \(f\): The number of vibrations per second. The unit is Hertz \([Hz]\).
5. Wave Speed \(v\): The speed at which the wave travels. The unit is meters per second \([m/s]\).
● The Magic Formula: \(v = f\lambda\)
The formula to find the speed of a wave is one of the most important in basic physics.
\(Speed = Frequency \times Wavelength\)
In other words,
\(v = f\lambda\)
Also, since frequency \(f\) and period \(T\) have an "inverse" relationship (\(f = \frac{1}{T}\)), you can also write it as:
\(v = \frac{\lambda}{T}\)
【Study Tip】
Recall the middle school concept "Speed = Distance \(\div\) Time." In the world of waves, "distance" corresponds to the wavelength \(\lambda\), and "time" corresponds to the period \(T\). Therefore, \(v = \frac{\lambda}{T}\), and if you rearrange this, you get \(v = f\lambda\)!
Summary: Definitely memorize \(v = f\lambda\)!
3. Transverse Waves and Longitudinal Waves
There are two types of waves based on their "direction of vibration."
● Transverse Waves
Waves where the medium vibrates perpendicular to the direction of wave propagation.
Examples: Waves on a string, light.
Since they look like wavy lines, they are easy to visualize.
● Longitudinal Waves
Waves where the medium vibrates parallel to the direction of wave propagation.
Examples: Sound, waves generated by pushing and pulling a spring.
Also called "Compressional waves." This is because they create areas of high density (compression) and low density (rarefaction) in the air.
【Trivia】
Earthquake tremors consist of "P-waves" and "S-waves." The small, rattling P-waves that arrive first are "longitudinal (Primary)," and the large, later-arriving S-waves are "transverse (Secondary)." These are the types of waves traveling through the Earth.
4. Superposition and Standing Waves
What happens when two waves collide?
● Principle of Superposition
When two waves overlap, the height at that location is the sum of the heights of the individual waves. After the waves pass through each other, they continue on in their original shape without being affected (the independence of waves).
● Standing Waves
When two waves with the same amplitude and wavelength approach from opposite directions and overlap continuously, they create a "wave that appears to stay in one place and vibrate." This is called a standing wave.
Antinode: The part that vibrates with the maximum amplitude.
Node: The part that does not vibrate at all.
【Point】
The "distance between adjacent nodes" of a standing wave is half (\(\frac{\lambda}{2}\)) of the original wavelength. This is a common target for test questions!
Summary: When waves traveling in opposite directions overlap, a "standing wave" is formed. The distance between nodes is half the wavelength!
5. Wave Reflection (Free End and Fixed End)
When a wave hits a wall and bounces back, it is called "reflection." There are two ways of reflecting depending on the state of the end.
1. Free End Reflection:
The end is free to move (like a string attached to a ring that slides along a rod). A crest reflects back as a crest.
2. Fixed End Reflection:
The end is firmly fixed in place. A crest reflects back as a trough (flipped upside down).
【Visualization】
For a fixed end, imagine the wave being pressed tightly against the wall; even if a crest tries to arrive, the wall pushes it back, forcing it to become a trough.
6. Properties of Sound
Finally, let's organize our thoughts on "sound," the most familiar wave.
● Three Elements of Sound
1. Loudness: The greater the amplitude \(A\), the louder the sound.
2. Pitch: The higher the frequency \(f\), the higher the pitch of the sound.
3. Timbre (Tone Quality): Even with the same pitch and loudness, different wave shapes result in different sounds (e.g., the difference between a piano and a guitar).
● Speed of Sound
The speed of sound \(V\) in air changes with temperature \(t\).
\(V = 331.5 + 0.6t [m/s]\)
When the temperature rises, air particles move around more vigorously, so the speed at which sound is transmitted increases slightly.
【Common Mistake】
"Shouting loudly makes sound travel faster" is a myth! Whether a voice is loud or quiet, the speed of sound does not change. The only thing that changes is the "amplitude."
Summary: Pitch is determined by frequency, and loudness is determined by amplitude!
Great work! That covers the basics of waves.
Start by getting comfortable with the calculations for \(v = f\lambda\). Try drawing diagrams when reading graphs, as this will deepen your understanding.
Once you understand physical waves, the way you see music and light will surely change. Keep moving forward at your own pace!