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, you need to use the formula v = λf, where v is the speed of the wave, λ is the wavelength, and f is the frequency.
First, let's find the wavelength (λ) using the given values of a, w, and k. In the given equation y = Asin(wt - kx), the term inside the sine function (wt - kx) represents the phase of the wave. For a plane wave, the phase is constant along any given x-axis or y-axis. Thus, wt - kx should be constant for all x values.
Since wt - kx should be constant, let's assume wt - kx = φ, where φ represents a constant phase.
Now, we can compare the given equation with the general equation of a plane wave, y = Asin(φ). Since wt - kx = φ, we can conclude that the phase angle φ in this case is wt - kx.
Comparing the general equation with the given equation, we can see that the amplitude (A) of the wave is a, the angular frequency (ω) is w, and the phase angle (φ) is wt - kx.
The phase velocity of the wave is given by v = ω / k.
Given:
a = 0.10 m
w = 8500 Hz
k = 25 / s
Substituting these values into the formula, we have:
v = w / k
v = 8500 Hz / 25 / s
v = 340 m/s
Therefore, the speed of the waves is 340 m/s.
To calculate the speed of the medium through which the wave is traveling, we can use the formula v = λf. The frequency (f) is given as 8500 Hz, and we have already calculated the speed (v) as 340 m/s.
v = λf
340 = λ * 8500
λ = 340 / 8500
λ = 0.04 m
Therefore, the wavelength of the wave is 0.04 m.
Now, let's move on to the equation of the reflected wave when the wave strikes a rigid boundary normally. In this case, the reflected wave will have the same amplitude as the incident wave, but the sign of the wave will be inverted. So, the equation of the reflected wave when this wave strikes a rigid boundary normally is:
y reflect = -Asin(wt - kx)
Note that the amplitude (A), angular frequency (ω), and wave number (k) remain the same as in the given equation. The only difference is the negative sign in front of the sine function.