A wave on a string is described by the equation y(x, t) = A sin(kx - ωt). What d
Practice Questions
Q1
A wave on a string is described by the equation y(x, t) = A sin(kx - ωt). What does 'k' represent?
Angular frequency
Wave number
Amplitude
Phase constant
Questions & Step-by-Step Solutions
A wave on a string is described by the equation y(x, t) = A sin(kx - ωt). What does 'k' represent?
Step 1: Understand the equation y(x, t) = A sin(kx - ωt). This equation describes a wave on a string.
Step 2: Identify the variables in the equation: 'A' is the amplitude, 'k' is the wave number, 'ω' is the angular frequency, 'x' is the position, and 't' is time.
Step 3: Focus on 'k'. The wave number 'k' tells us how many wavelengths fit into a unit of distance.
Step 4: The relationship between the wave number 'k' and the wavelength 'λ' is given by the formula k = 2π/λ.
Step 5: This means that if you know the wavelength of the wave, you can find 'k' by using the formula.
Wave Number – The wave number 'k' represents the spatial frequency of the wave, defined as the number of wavelengths per unit distance, and is inversely related to the wavelength (λ) by the formula k = 2π/λ.
