1. General Wave Equation:
* v = fλ
* v: Wave speed (m/s)
* f: Frequency (Hz)
* λ: Wavelength (m)
This equation tells us that the speed of a wave is directly proportional to its frequency and wavelength.
2. Specific Wave Types:
* Transverse waves on a string:
* v = √(T/μ)
* T: Tension in the string (N)
* μ: Linear mass density (mass per unit length) of the string (kg/m)
* Sound waves in air:
* v = √(γP/ρ)
* γ: Adiabatic index (ratio of specific heats) for air (approximately 1.4)
* P: Pressure of the air (Pa)
* ρ: Density of the air (kg/m³)
* Light waves (electromagnetic waves) in a vacuum:
* v = c
* c: Speed of light in vacuum (approximately 299,792,458 m/s)
Important Points:
* Medium dependence: The speed of a wave is determined by the properties of the medium it travels through. For example, sound travels faster in solids than in liquids, and faster in liquids than in gases.
* Frequency and wavelength: The relationship between frequency and wavelength is always v = fλ, but the actual values of f and λ can change depending on the medium.
Example:
Let's say you have a wave traveling on a string with a tension of 100 N and a linear mass density of 0.05 kg/m. Using the equation for transverse waves on a string:
* v = √(100 N / 0.05 kg/m) = √2000 m²/s² = 44.7 m/s
This means the wave will travel at 44.7 meters per second on that string.
