Study Notes on Waves and Energy Transport

6.2 Waves

6.2.1 Exploring Waves

  • Waves can be explored using a long spring attached to a wall.

  • Action Steps:

    • Hold the other end of the spring and make a quick up-and-down motion.

    • Observe the pulse moving along the spring.

    • Move your hand up and down in a steady rhythm.

    • Questions to Consider:

    • In which direction do the oscillations move?

    • In which direction does the wave move?

    • Can you make the wave and oscillations move in the same direction?

6.2.2 Periodic Phenomena

  • Certain phenomena repeat at regular intervals, known as periodic phenomena.

  • These recurring phenomena are called oscillations.

  • Waves are defined as oscillations that spread out in space.

6.2.3 Characteristics of Oscillations

  • Examples of oscillation include:

    • Trees swaying in the wind.

    • Your arms swinging while walking.

  • Definition of an oscillation:

    • A periodic motion between two extreme positions.

  • Experiment with oscillations:

    • Hang a weight from a spring.

    • Pull the weight slightly down and release it to observe oscillations.

  • Period (T): the time taken to complete one full oscillation from one extreme position and back to the same extreme position.

  • Equilibrium position: where the weight hangs at rest.

6.2.4 Displacement and Amplitude

  • Displacement refers to the distance from the equilibrium position.

  • Displacement varies over time.

  • The maximum positive displacement is called the amplitude.

  • Attach a pen to the weight and draw a constant speed paper past it.

    • As the weight oscillates, the pen traces a curve showing how displacement changes over time.

  • The curve on the paper shows how to read period and amplitude from it.

    • Period (T): time taken for one complete oscillation.

    • Amplitude: largest displacement from the equilibrium position.

6.2.5 Waves and Frequencies

  • Definition of waves:

    • Waves occur when something oscillates back and forth around an equilibrium position.

  • When the period is known, frequency can be calculated.

  • Frequency (f): number of oscillations per second, measured in hertz (Hz).

  • Example 1: Calculating Wave Frequencies

    • If you observe a cork bobbing up and down in water, one can measure its oscillation frequency.

    • Counting how many times the cork reaches the top in 10 seconds:

    • If it bobs 15 times in 10 seconds:

      • Period (T) calculation: T = \frac{10s}{15} = 0.67s

      • Frequency (f) calculation: f = \frac{15}{10s} = 1.5s^{-1} = 1.5Hz.

6.2.6 Wave Characteristics

  • Waves in water consist of wave crests and troughs.

  • Wavelength (位): the distance between two consecutive wave crests.

  • Example of waves:

    • Small stone thrown into water resulting in wavelength of a few centimeters.

    • During a storm, one can observe waves as much as one hundred meters long.

6.2.7 Amplitude, Frequency, and Wavelength

  • In summary:

    • Wavelength is the distance between two adjacent wave crests.

    • Frequency is the number of oscillations per second, measured in hertz (Hz).

    • Amplitude is the maximum displacement from the equilibrium position.

Resonance

6.3.1 Exploring Resonance

  • Explore resonance using a crystal glass:

    • Rubbing a wet finger on the rim of a glass to produce sound.

    • An opera singer singing the same tone can shatter the glass.

    • Consider the experience of jumping on a diving board:

    • The board may sway in sync with your jumps, causing larger oscillations when jumping at a specific frequency.

6.3.2 Eigenfrequency

  • Shorter individuals often have a quicker walking pace than taller individuals due to their limbs swinging at their own eigenfrequency.

  • Definition of eigenfrequency:

    • The frequency at which a swing system oscillates when left to swing freely.

  • When a swinging system is driven by a periodic force of the same frequency as its eigenfrequency, resonance occurs, producing larger amplitudes.

6.3.3 Engineering Considerations

  • Engineers must consider the eigenfrequency of different systems to prevent resonance:

    • Cars must avoid resonating parts while driving.

    • Bridges must be designed considering eigenfrequencies to avoid catastrophic failures (e.g., Tacoma Narrows Bridge collapse due to resonance in 1940).

Types of Waves

6.4.1 Transverse and Longitudinal Waves

  • Transverse Waves:

    • Direction of wave propagation is perpendicular to particle motion.

    • Example: In the spring experiment, waves travel along the length of the spring while each point oscillates up and down.

  • Longitudinal Waves:

    • Direction of wave propagation is parallel to particle motion.

    • Example: Pulling a spring back and forth creates longitudinal waves.

    • Sound in air is a longitudinal wave consisting of compressions and rarefactions.

6.4.2 Mechanical Waves

  • Mechanical waves require a medium to propagate (e.g., sound waves).

    • Example of mechanical waves includes sound waves, which necessitate substance; sound cannot exist in a vacuum.

  • Seismic waves are also examples of mechanical waves.

  • Electromagnetic Waves:

    • Comprise oscillating electric and magnetic fields.

    • Can propagate through a vacuum (e.g., light, radio waves).

Energy Transport in Waves

6.5.1 Energy in Sine Waves

  • Energy comes from a wave source.

  • If a weight oscillates freely, the amplitude of the oscillation diminishes due to opposing forces like friction and air resistance.

6.5.2 Wave Speed

  • Definition of wave speed: a measure of how quickly oscillations spread.

    • Wave speed equals the rate at which energy propagates.

  • There is a relationship among wave speed (v), frequency (f), and wavelength (位):

    • v = f \cdot \lambda

6.5.3 Example of Sound Waves

  • Kammertone A corresponds to a frequency of 440 Hz.

    • Sound speed in air approximately 330 m/s.

    • Calculation of wavelength results in:

    • \lambda = \frac{v}{f} = \frac{330 m/s}{440 1/s} = 0.75 m (75 cm).

6.5.4 Speed of Light

  • Light, an electromagnetic radiation, travels at:

    • c = 300,000 km/s in a vacuum.

    • Relationship among speed of light (c), frequency (f), and wavelength (位):

    • c = f \cdot \lambda.

    • Higher frequency correlates to shorter wavelength; low wavelength implies high frequency.

6.5.5 Electromagnetic Radiation

  • Definition of electromagnetic radiation: does not require a medium, travels at light speed.

  • Example: Light from Andromeda Galaxy travels approximately 2.5 million light years to Earth.

Reflection and Refraction

6.6.1 Reflection Phenomenon

  • Reflection occurs when light bounces back from a surface, similar to a ball off a wall.

  • Law of reflection states:

    • Angle of incidence (\alphai) equals angle of reflection (\alphar).

    • \alphai = \alphar.

6.6.2 Refraction Phenomenon

  • An example of wave direction change when moving from deep water to shallow:

    • Waves slow down, and thus change direction as they approach the shore due to variable wave speed in different depths.

    • Similarly, light refracts when passing from air to glass due to the interaction of light with denser materials,
      resulting in changes in speed.

6.6.3 Everyday Applications

  • Light refraction is utilized in lenses and glasses.

Wave Phenomena

6.7.1 Diffraction and Interference

  • Waves diffract when passing through openings.

  • Example: Sound from a speaker bends around open doors or walls which causes better sound transmission.

  • Absorption: Sound may lose energy when passing through walls, converting some energy to molecular motion in the wall.

6.7.2 Wireless Communication and Waves

  • Waves are utilized in various wireless technologies (e.g., TV remotes, mobile phones).

  • Questions to Consider:

    • Can a remote control work through a wall or bend around a corner?

6.7.3 Interference of Waves

  • Conflict between waves can create an interference pattern (

    • The resultant displacement is the sum of individual wave displacements.

    • Example: Noise-canceling headphones generate 'anti-noise' to reduce sound interference.

    • Wireless communication can experience interference, especially at common frequencies like 2.4 GHz.

The Electromagnetic Spectrum

6.8.1 Overview of the Spectrum

  • Electromagnetic waves span a vast range of wavelengths from very long (hundreds of thousands of meters) to extremely short (less than a millionth of a millimeter).

  • Visible light is just a small fraction of the entire electromagnetic spectrum.

6.8.2 Types of Electromagnetic Waves

  • Radio Waves: Wavelengths from 1 mm to over 10,000 m.

  • Microwaves: Essentially short radio waves, heavily used in wireless communication.

  • Infrared Radiation (IR): Responsible for heat; emitted by all objects based on temperature.

  • Visible Light: The segment perceived by the human eye, 400 nm to 700 nm.

  • Ultraviolet Light (UV): The sun emits UV radiation that can propagate into the skin, divided into three categories based on wavelength (UVA, UVB, UVC).

  • X-rays: Utilized in medical imaging; penetrate soft tissue but not bones.

  • Gamma Rays: Exhibit the highest energy and shortest wavelength, used in cancer treatment.

6.8.3 Ionizing Radiation

  • UVC, X-rays, and gamma rays are examples of ionizing radiation, which can disrupt atomic structures, potentially causing cellular damage and diseases such as cancer.