The equation y=As in(wt-kx)represents a
plane wave traveling along the x-direction. If
a=0.10m, w=8500hz and k=25/secs......Calculate
the speed of the Waves
-Calculate the speed of the medium through
which the wave is travelingl -What is the equation of the reflected wave
produced when thisv wave strikes a rigid
boundary normally?
To calculate the speed of the waves, we can use the formula:
v = λ * f
where v is the speed of the waves, λ is the wavelength, and f is the frequency.
We need to find the wavelength (λ) first. In the equation y = Asin(wt - kx), the term (wt - kx) represents the phase of the wave. The phase is given as 0 because it's a plane wave traveling along the x-direction. Therefore, we can rewrite the equation as:
y = Asin(-kx)
Comparing this with the standard equation of a sinusoidal wave:
y = Asin(kx)
We can see that the wavelength (λ) is equal to 2π/k.
Now, let's calculate the wavelength:
λ = 2π/k = 2π/(25/sec) = 0.08 m
Next, we can substitute the values of wavelength (λ) and frequency (f) into the equation to find the speed (v):
v = λ * f = (0.08 m) * (8500 Hz) = 680 m/s
So, the speed of the waves is 680 m/s.
To calculate the speed of the medium through which the waves are traveling, we can use the formula:
v = λf
Rearranging the formula, we get:
v = λ * f
Substituting the values of wavelength (λ) and frequency (f) into the equation:
v = (0.08 m) * (8500 Hz) = 680 m/s
So, the speed of the medium through which the waves are traveling is 680 m/s.
When a wave strikes a rigid boundary normally, it reflects without any change in direction. The reflected wave has the same frequency and wavelength as the incident wave but moves in the opposite direction. The equation for the reflected wave can be written as:
y = -Asin(wt + kx)
So, the equation of the reflected wave is y = -Asin(wt + kx).