A traveling wave has displacement D(x,t)=(3.00cm)sin(5.36x-6.71t), where x is in meters and t is in seconds. What is the wave speed of this wave?
**snapshot graph at t=1/4 s
v = omega/k
The wave equation is of the form
D(x,t) = A*sin(k*x-omega*t)
k = 5.36
omega = 6.71
solve for v, the wave speed
To determine the wave speed, we need to identify the equation that relates wave speed to the given information. In this case, we can use the equation:
v = λ * f
where:
v is the wave speed,
λ (lambda) is the wavelength of the wave, and
f is the frequency of the wave.
To find the wave speed, we need to extract the wavelength and frequency from the given equation of displacement. The equation is:
D(x,t) = (3.00 cm) * sin(5.36x - 6.71t)
To determine the wavelength, we can examine the coefficient of the x-term in the argument of the sine function (5.36).
λ = 2π / k
where k is the coefficient of the x-term in the argument of the sine function.
Using the given value of k = 5.36, we can calculate the wavelength:
λ = 2π / 5.36 = 2π / (5.36 m^(-1)) ≈ 1.17 m
Next, to calculate the frequency, we need to examine the coefficient of the t-term in the argument of the sine function (-6.71).
f = k / (2π)
where k is the coefficient of the t-term in the argument of the sine function.
Using the given value of k = -6.71, we can calculate the frequency:
f = -6.71 / (2π) ≈ -1.07 Hz
It's important to note that the negative sign arises due to the direction of the wave propagation in this equation.
Now, to find the wave speed (v), we can substitute the calculated values of wavelength (λ) and frequency (f) in the wave speed equation:
v = λ * f
v = (1.17 m) * (-1.07 Hz) ≈ -1.25 m/s
Therefore, the wave speed for the given traveling wave is approximately -1.25 m/s.
**Unfortunately, since the snapshot graph at t=1/4 s is not provided, we are unable to provide a precise graphical representation at that time instant. However, the displacement equation D(x,t) = (3.00 cm) * sin(5.36x - 6.71t) enables us to calculate the wave speed.