A wave traveling along a string is described by the equation y(x, t) = A sin(kx - ωt). What does 'k' represent?
Practice Questions
1 question
Q1
A wave traveling along a string is described by the equation y(x, t) = A sin(kx - ωt). What does 'k' represent?
Amplitude
Wave number
Frequency
Angular frequency
'k' is the wave number, which is related to the wavelength λ by the equation k = 2π/λ.
Questions & Step-by-step Solutions
1 item
Q
Q: A wave traveling along a string is described by the equation y(x, t) = A sin(kx - ωt). What does 'k' represent?
Solution: 'k' is the wave number, which is related to the wavelength λ by the equation k = 2π/λ.
Steps: 6
Step 1: Understand that the equation y(x, t) = A sin(kx - ωt) describes a wave.
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: Recognize that 'k' is called the wave number.
Step 4: Learn that the wave number 'k' tells us how many wave cycles fit into a unit of distance.
Step 5: Know that 'k' is related to the wavelength (λ) of the wave by the formula k = 2π/λ.
Step 6: Conclude that 'k' helps us understand the spatial characteristics of the wave.
