General: Semester 4: (Physics) Generic Elective Course 4 (University of Calcutta): (2024 spring semester course)

Handwritten notes are available below.

• Wave:

  • • Trigonometric formulas [link] (Find more relevant ones and add them here.)

    • SHM [link]

    • Superposition of two harmonic oscillators:  collinear + perpendicular; Lissajous curve (see figures below; the exact shape and directional arrow depend on whether you use the cosine or sine function)  [link]

    • Damped vibration + loudness [link] [link of shorter version]

    • Forced vibration [link]

    • Travelling wave + standing wave + string (+ Plucked + stucked string) [link]

-------------------------------------------

Bel (B): 

a logarithmic unit measuring acoustic power (or intensity). One decibel corresponds to the power (or intensity) of the source is 1 pico watts (or 1 pico watts/ meter^2). 

The decibel level L is calculated using:
L B= log_{10}  [I/I_0], where I_0 is 10^{-12} watts/meter^2. 

Loudness vs. Intensity of Sound: 

Loudness: 

• This is a subjective perception of sound by the human ear.  

• Human ears are more sensitive to certain frequencies (typically around 2,000 to 4,000 Hz), so a sound of the same intensity can be perceived as louder or softer depending on its frequency. 

• Loudness can vary from person to person and is often measured in phons or sones.

Intensity: 

• This is an physical quantity that measures the power per unit area of a sound wave. 

• The intensity of a sound wave is a measure of the energy it carries and is independent of the frequency. 

• It is purely a physical measure of the sound wave's power.

Differences Between Prism Spectra and Grating Spectra:

Prism Spectra: 

• Uses refraction to separate light. Different wavelengths bend by different amounts due to varying refractive indices. 

• Non-linear dispersion. Shorter wavelengths are more closely packed than longer wavelengths.

Grating Spectra: 

• Uses diffraction and interference to separate light. Light is diffracted at specific angles based on the wavelength and grating spacing.

• Nearly linear dispersion. Wavelengths are more evenly spaced, providing more accurate wavelength measurements.

Acoustic resonance

Acoustic resonance is a phenomenon where an acoustic system amplifies sound waves that match one of its natural frequencies of vibration. In a forced simple harmonic motion (SHM) oscillator, if the external force has an angular frequency (ω) equal to the natural angular frequency (ω₀) of the oscillator (ω = ω₀), both the amplitude (in the absence of damping or with negligible damping) and the velocity amplitude of the system reach their maximum. This is known as acoustic resonance.

What is the difference between interference and diffraction?

1. Definition: When monochromatic waves of light from two sources proceed almost in the same direction and superpose at a point either in same or in opposite phase. Then the intensity of light at that point will be maximum or minimum according to the waves meet the point in the same or in the opposite phase. This phenomenon is known as interference of light. This phenomenon requires for its explanation that light must have a wave nature.

When light from a narrow linear slit is incident on the sharp edge of an obstacle, it will be found that there is illumination to some extent within the geometrical shadow of the obstacle. This shows that light can bend around an obstacle. All phenomena like this which are produced when the incident wavefront is somehow limited are called diffraction of light.

2. Condition:  Due to interference, we can find alternative bright (constructive) and dark (destructive) regions of illumination. For this we need two coherent light sources. 

Diffraction patterns involve a central maximum surrounded by a minimum, then another maximum of diminishing amplitude, and so on. Diffraction can occur when a single light source encounters an obstacle.

-------------------------------------------

• Optics:

  • • Huygens–Fresnel principle  + wavefront [link] (note: last two pages you may not need to read -  it is proof of laws of reflection using Huygens' principle)

    • Interference of light + Stroke's law+ Newton's ring [link] (Homework: Find the differences in the interference fringes formed using Fresnel's biprism and Lloyd's mirror.)

    • Fresnel Difraction: Half-period zones + Zone plate [link]

    • Fraunhofer Diffraction at single slit [link]

    • Fraunhofer Diffraction at double slit [link]

    • Fraunhofer Diffraction at diffraction grating [link]

    • Polarization + Malu's Law + Nicol prism [link]