Wave phenomena encompass a wide array of physical behaviors and characteristics of waves. In the International Baccalaureate (IB) Physics syllabus, particularly for the higher level (HL) students, understanding these phenomena is crucial. This study note will cover key topics such as wavefronts, simple harmonic motion (SHM), single-slit diffraction, interference, resolution, and the Doppler effect. Each section will break down complex ideas into smaller, digestible parts and include examples to solidify understanding.
Consider transverse waves traveling in a horizontal plane. The distance between successive wavefronts equals the wavelength ($\lambda$) of the waves.
A common experiment to demonstrate wave phenomena such as diffraction involves using a ripple tank.
Tip:
Ripple tanks are useful for visualizing wave behaviors such as reflection, refraction, and diffraction.
SHM can be described by the equation:
$$ a = -\omega^2 x $$
where:
The total mechanical energy in SHM is conserved and given by:
$$ E = \frac{1}{2} m \omega^2 A^2 $$
where:
Example:
A child on a swing performs 0.2 oscillations per second. Calculate the period of the child's oscillations.
Solution:
Diffraction occurs when waves pass through a narrow opening and spread out. The intensity pattern is characterized by a central maximum with successive minima and maxima.
The intensity $I$ at a point on the screen is given by:
$$ I = I_0 \left( \frac{\sin(\beta)}{\beta} \right)^2 $$
where:
This experiment demonstrates the principle of superposition, where two coherent light waves produce an interference pattern of bright and dark fringes.
For a diffraction grating, the condition for constructive interference is given by:
$$ d \sin(\theta) = n\lambda $$
where:
The Rayleigh criterion defines the limit of resolution for two point sources. It states that two sources are resolvable when the principal maximum of one diffraction pattern coincides with the first minimum of the other.
The minimum resolvable angle $\theta$ is given by:
$$ \theta = 1.22 \frac{\lambda}{D} $$
where:
The Doppler effect describes the change in frequency and wavelength of a wave as observed by someone moving relative to the source.
Wavefront diagrams can visualize the Doppler effect. For a moving source:
Example:
A police siren emits a sound at a frequency of 700 Hz. If the police car is moving towards a stationary observer at a speed of 30 m/s, calculate the observed frequency. (Speed of sound = 343 m/s)
Solution:
Wave phenomena encompass a variety of behaviors essential for understanding physics at the higher level. From wavefronts and SHM to diffraction, interference, resolution, and the Doppler effect, each concept builds upon the fundamental properties of waves. Mastery of these topics is crucial for success in the IB Physics HL syllabus.