Waves

Waves

Traveling Waves

• Waves are rhythmic disturbances that carry energy through matter or space.
• Waves transfer energy, not matter.
• Most waves are created by vibrations.
• A wave pulse is a single impulse.

Transverse Waves

• Transverse waves are waves in which particles move perpendicularly to the direction the wave moves.
• They look like sine curves.
• Wave energy moves left to right, while oscillation occurs up and down.
• Examples of transverse waves: radio waves, microwaves, infrared radiation, visible light, ultraviolet radiation, X-rays, gamma rays, and surfing waves.

Parts of Transverse Waves

• Crest: The top of a wave.
• Trough: The bottom of a wave.
• Wavelength ($\lambda$): The distance between successive parts of a wave (crest-to-crest or trough-to-trough).
• Amplitude: The distance from the normal resting position to the top of the crest or the bottom of the trough.
• Node: A point of zero amplitude, representing the rest position.
• Antinode: A point of maximum amplitude, which is either the crest or the trough.

Compression Waves

• Longitudinal waves, also known as compression waves, are waves in which particles move parallel to the direction the wave moves.
• Oscillations occur in the same direction as wave movement.
• Wave energy moves left to right, with oscillation also occurring left to right.
• Examples: sound waves, some earthquakes, and tsunamis in the ocean.

Parts of Compression Waves

• Compression: An increase in medium density.
• Rarefaction: A decrease in medium density.
• Wavelength ($\lambda$): The distance between successive parts of a wave (compression-to-compression or rarefaction-to-rarefaction).

Frequency & Period

• Wavelength ($\lambda$): The distance from crest-to-crest or trough-to-trough, representing one full cycle. Its units are meters.
• Frequency: The number of cycles (or oscillations) per second.
  • Units: Hertz (Hz), equivalent to 1/second.
  • Symbol: f
  • The frequency of a wave is determined by the period of the wave.
• Period: The time it takes for one cycle.
  • Units: seconds.
  • Symbol: T

Example: Red Light

• A red color's frequency is $10^{15}$ Hz. To find the period:
  • $f = 10^{15} \text{ Hz}$
  • $T = \frac{1}{f}$
  • $T = \frac{1}{10^{15} \text{ Hz}} = 1.0 \times 10^{-15} \text{ seconds}$

Speed of a Wave

• The speed of a wave is the distance it moves over time.
• Determined by the medium through which the wave moves.
• Formula: $v = f \lambda$
  • v = velocity (m/s)
  • f = frequency (Hertz = waves/sec)
  • $\lambda$ = wavelength (meters / wave)

Example 1: Transverse Wave in a String

• Given: The speed of a transverse wave in a string is 15.0 m/s, and the frequency is 5.00 Hz. Find the wavelength.
  • $v = 15 \text{ m/s}$
  • $f = 5 \text{ Hz}$
  • $v = f \lambda \implies \lambda = \frac{v}{f}$
  • $\lambda = \frac{15 \text{ m/s}}{5 \text{ Hz}} = 3 \text{ meters/wave}$

Example 2: Wave in a Slinky

• Given: A wave with a frequency of 20.0 Hz travels along a slinky, and the distance between successive compressions is 0.400 m. Find the speed of the wave.
  • $f = 20 \text{ Hz}$
  • $\lambda = 0.4 \text{ m/wave}$
  • $v = f \lambda$
  • $v = 20 \text{ Hz} \times 0.4 \text{ m/wave} = 8 \text{ m/s}$

Example 3: Sound Wave

• Given: A sound wave has a frequency of 262 Hz and a wavelength of 1.29 m. Find the speed, the time it takes to travel the length of a 91.4 m football field, and the period of the wave.
  • $f = 262 \text{ Hz}$
  • $\lambda = 1.29 \text{ m/wave}$
  • $d = 91.4 \text{ m}$
  • $v = f \lambda = 262 \text{ Hz} \times 1.29 \text{ m/wave} = 337.98 \text{ m/s}$
  • $t = \frac{d}{v} = \frac{91.4 \text{ m}}{337.98 \text{ m/s}} = 0.27 \text{ seconds}$
  • $T = \frac{1}{f} = \frac{1}{262 \text{ Hz}} = 0.0038 \text{ seconds}$

Standing Waves

• Node: A point where the combined wave doesn’t move.
• Antinode: A point where the displacement is greatest.