This chapter introduces the concept of waves and their significance in physics, illustrating how they transport energy and information through different media.
Waves – Formula & Equation Sheet
Essential formulas and equations from Physics Part - II, tailored for Class 11 in Physics.
This one-pager compiles key formulas and equations from the Waves chapter of Physics Part - II. Ideal for exam prep, quick reference, and solving time-bound numerical problems accurately.
Key concepts & formulas
Essential formulas, key terms, and important concepts for quick reference and revision.
Formulas
v = fλ
v is the wave speed (m/s), f is the frequency (Hz), and λ is the wavelength (m). This formula relates the speed of a wave to its frequency and wavelength, useful in both sound and light wave contexts.
T = μv²
T is the tension (N), μ is the linear mass density (kg/m), and v is the wave speed (m/s). This formula gives the relationship for the speed of waves on a string under tension.
v = √(B/ρ)
v is the speed of sound (m/s), B is the bulk modulus (Pa), and ρ is the density (kg/m³). This is applicable to longitudinal waves in fluids and helps understand sound propagation.
ν = 1/T
ν is the frequency (Hz), and T is the period (s). This fundamental relationship shows how frequency and period are inversely related.
λ = v/f
λ is the wavelength (m), v is the wave speed (m/s), and f is the frequency (Hz). This formula allows calculation of wavelength from speed and frequency.
s(x, t) = a sin(kx - ωt)
s is the displacement in a longitudinal wave (m), a is the amplitude (m), k is the wave number (rad/m), and ω is the angular frequency (rad/s). This gives the displacement of particles in a longitudinal wave.
y(x, t) = a sin(kx - ωt)
y is the displacement in a transverse wave, k is the wave number (rad/m), ω is the angular frequency (rad/s), and a is the amplitude of the wave. This equation describes the motion of a wave on a string.
k = 2π/λ
k is the wave number (rad/m) and λ is the wavelength (m). This formula connects the spatial frequency of the wave with its wavelength.
ω = 2πf
ω is the angular frequency (rad/s) and f is the frequency (Hz). This relationship is important in oscillatory motion and wave equations.
A(φ) = 2a cos(φ/2)
A is the amplitude of the resultant wave, a is the amplitude of the constituent waves, and φ is the phase difference. This is crucial for understanding interference effects between two waves.
Equations
y(x, t) = 2a sin(kx) cos(ωt)
This is the standing wave equation resulting from the superposition of two waves traveling in opposite directions. It indicates the formation of nodes and antinodes in stationary waves.
v = √(T/μ)
v is the speed of a transverse wave on a string, T is the tension (N), and μ is the linear mass density (kg/m). This equation describes how tension and mass density affect wave speed.
P = dF/dA
P is the pressure (Pa), F is the force (N), and A is the area (m²). This fundamental definition of pressure is important for understanding sound propagation in fluids.
B = ρv²
B is the bulk modulus (Pa), ρ is the density (kg/m³), and v is the speed of sound (m/s). This relation defines how fluids resist compression.
y1 = A sin(kx - ωt + φ1)
y1 describes one of the two interfering waves. φ1 denotes its phase, and A is its amplitude. Used in problems involving wave interference.
y2 = A sin(kx - ωt + φ2)
y2 describes the second wave, with a possibly different phase φ2 compared to y1. This allows analysis of how two waves combine.
R = (Z2 - Z1)/(Z2 + Z1)
R is the reflection coefficient, while Z1 and Z2 are the acoustic impedances of the two media. This indicates how much of a wave is reflected at a boundary.
y = H sin(kx - ωt)
This formula represents a harmonic wave traveling in the medium, with H being its height, which can vary in observational studies.
x = λn/2L
x expresses the position of nodes or antinodes along a stretched string of length L vibrating in the nth harmonic. Important for understanding standing waves.
ν = c/λ
Where ν is the frequency (Hz) and c is the speed of the wave in a medium. This is essential in wave mechanics for relating frequency, speed, and wavelength.
This chapter explores the mechanical properties of fluids, including their behavior under various forces and conditions. Understanding these properties is essential for applications in engineering and environmental science.
Start chapterThis chapter explores the thermal properties of matter, focusing on heat, temperature, and heat transfer mechanisms. Understanding these concepts is vital for grasping how energy interacts with materials in various states.
Start chapterThis chapter covers the fundamental laws of thermodynamics, focusing on heat, work, and energy transfer in systems.
Start chapterThis chapter explains the kinetic theory of gases, detailing how gas behaves due to the movement of its molecules. Understanding this theory is fundamental for grasping the properties of gases and their interactions.
Start chapterThis chapter explores the concept of oscillations, including periodic and oscillatory motions which are fundamental to understanding various physical phenomena.
Start chapter
