IB MYP 4-5 Physics- Properties of waves- Study Notes - New Syllabus
IB MYP 4-5 Physics-Properties of waves- Study Notes
Key Concepts
- Properties of waves
Properties of Waves
Properties of Waves
Wavelength (\(\lambda\)): The distance between two consecutive points in phase (e.g., two crests or two compressions).
Unit: meter (m)
Amplitude (A): The maximum displacement of particles from their equilibrium position. It indicates the wave’s energy.
Larger amplitude → more energy.
Frequency (f): The number of complete wave cycles passing a point per second.
Unit: hertz (Hz)
Period (T): The time taken for one complete cycle of the wave.
\(T = \dfrac{1}{f}\)
Wave speed (v): The distance traveled by the wave per unit time.
Formula: \(v = f \lambda\)
- Phase: The fraction of a cycle a wave has completed at a point, relative to a reference.
- Reflection: The bouncing back of waves when they strike a barrier.
- Refraction: The bending of waves when moving from one medium to another due to speed change.
- Diffraction: The spreading of waves when they pass through a narrow gap or around edges.
- Interference: When two waves overlap, producing constructive or destructive interference patterns.
- Polarization (only for transverse waves): Restriction of wave vibrations to one direction.
Example:
A wave has a frequency of \(50 \, \text{Hz}\) and a wavelength of \(0.2 \, \text{m}\). Find its speed.
▶️ Answer/Explanation
Using \(v = f \lambda\):
\(v = 50 \times 0.2 = 10 \, \text{m/s}\)
Final Answer: \(\boxed{10 \, \text{m/s}}\)
Example:
The period of a wave is \(0.01 \, \text{s}\). What is its frequency?
▶️ Answer/Explanation
Using \(f = \dfrac{1}{T}\):
\(f = \dfrac{1}{0.01} = 100 \, \text{Hz}\)
Final Answer: \(\boxed{100 \, \text{Hz}}\)
Example:
A light wave in air has a frequency of \(6 \times 10^{14} \, \text{Hz}\). If the speed of light is \(3 \times 10^8 \, \text{m/s}\), find the wavelength.
▶️ Answer/Explanation
Using \( \lambda = \dfrac{v}{f} \):
\( \lambda = \dfrac{3 \times 10^8}{6 \times 10^{14}} = 5 \times 10^{-7} \, \text{m}\)
Final Answer: \(\boxed{500 \, \text{nm}}\) (which is visible light)
The Wave Equation
The wave equation relates the speed of a wave to its frequency and wavelength.
\( v = f \lambda \)
- Where:
- \(v\) = wave speed (m/s)
- \(f\) = frequency (Hz)
- \(\lambda\) = wavelength (m)
Key points:
- As frequency increases, wavelength decreases (if speed is constant).
- Wave speed depends on the medium (e.g., light travels slower in glass than in air).
- All electromagnetic waves travel at the same speed in vacuum:
\(c = 3 \times 10^8 \, \text{m/s}\)
Example:
A wave has a frequency of \(200 \, \text{Hz}\) and a wavelength of \(1.5 \, \text{m}\). Find its speed.
▶️ Answer/Explanation
Using \(v = f \lambda\):
\(v = 200 \times 1.5 = 300 \, \text{m/s}\)
Final Answer: \(\boxed{300 \, \text{m/s}}\)
Example:
A water wave travels at \(4 \, \text{m/s}\) with a frequency of \(2 \, \text{Hz}\). Find the wavelength.
▶️ Answer/Explanation
Using \( \lambda = \dfrac{v}{f} \):
\(\lambda = \dfrac{4}{2} = 2 \, \text{m}\)
Final Answer: \(\boxed{2 \, \text{m}}\)
Example:
Light has a frequency of \(6 \times 10^{14} \, \text{Hz}\). Calculate its wavelength in vacuum.
▶️ Answer/Explanation
Using \( \lambda = \dfrac{v}{f} \):
\(\lambda = \dfrac{3 \times 10^8}{6 \times 10^{14}} = 5 \times 10^{-7} \, \text{m}\)
Final Answer: \(\boxed{500 \, \text{nm}}\) (green light)