a). The displacement of a wave travelling in the positive x-direction is D(x,t)=(5.94cm)sin(1.18x-132.6t), where x is in meters and t is in seconds. What is the frequency?
b). What is its wavelength?
c).What is the speed of the wave?
To find the answers to these questions, we need to understand the equations related to waves and their properties.
a) The equation for a wave is given by D(x,t) = A * sin(kx - ωt), where A represents the amplitude, k is the wave number, x is the position of the wave, ω is the angular frequency, and t is the time.
Comparing the given equation to the standard equation, we can determine the values of k and ω in order to find the frequency.
In this case, k = 1.18 and ω = 132.6. The frequency (f) of the wave is related to the angular frequency by the equation f = ω / (2π).
To find the frequency, we need to divide the angular frequency by 2π:
f = 132.6 / (2π) = 21.1 Hz
Therefore, the frequency of the wave is 21.1 Hz.
b) The wavelength (λ) of a wave is the distance between two consecutive points in a wave that are in phase with each other. In this case, we need to find the value of k to determine the wave number and therefore the wavelength.
The wave number is given by k = 2π / λ. Rearranging this equation, we find that the wavelength is λ = 2π / k.
From the given equation, we know that k = 1.18. Plugging this value into the equation, we have:
λ = 2π / 1.18 ≈ 5.33 m
Therefore, the wavelength of the wave is approximately 5.33 meters.
c) The speed of a wave (v) is related to its frequency (f) and wavelength (λ) by the equation v = λf.
From the previous calculations, we have found the values of f = 21.1 Hz and λ = 5.33 m:
v = 5.33 * 21.1 = 112.3 m/s
Therefore, the speed of the wave is approximately 112.3 m/s.