A transverse traveling-wave on a cable is represented by D = 0.53 sin(5.6x + 84t) in which D and x come in yards and t is within moments.
Is in reality quite easy as soon as you learn the offered revolution displacement equation.
So that you’re offered D = .53sin(5.6x + 84t), which can be in structure Asin((2π/λ)x + (2πƒ)t), for a revolution transferring the unfavorable x path, which this 1 is.
(a) as you can plainly see from taking a look at the formatted equation, the things before x, 5.6, is equivalent to (2π/λ).
5.6 = 2π/λ
λ (the Greek-letter lambda, popular to denote wavelength) = 2π/5.6 = 1.12 m
(b) likewise, the things before t, 84, is equivalent to (2πƒ).
84 = 2πƒ
ƒ (regularity) = 84/2π = 13.37 Hz
(c) The velocity of a revolution, or “phase velocity,” printed in regards to regularity and wavelength, is λƒ.
v = λƒ = (1.12)(13.37) = 14.97 m/s
(d) that one’s a breeze. The formatted equation reveals that the things as you’re watching sin purpose will be your amplitude, A.
A = .53
(age) that one I happened to be having some difficulty with, but we sooner or later figured it after overview of my records. You may be offered a function, D(x, t), which can be a situation purpose, proper? Really, I’m certain do you know what the by-product of a situation purpose is. A velocity purpose!
The by-product regarding the formatted purpose is V(0, t) = A(2πƒ)cos((2πƒ)t) (we are using it at x=0 to create choosing the max velocity feasible), where in actuality the (2πƒ) up in front arises from the by-product regarding the things in the cos purpose. The by-product of (2πƒ)t is (2πƒ), which can be after that increased because of the whole Acos((2πƒ)t), providing the outcome A(2πƒ)cos((2πƒ)t).
Therefore, exactly what performed that inform you? Well, absolutely nothing, however. What you need to do is sub in 0 for t to get the max velocity.
V = A(2πƒ)cos((2πƒ)(0))
V = A(2πƒ)cos(0)
V = A(2πƒ) = Vmax = .53(2π(13.37)) = 44.52 m/s
After that, your Vmin merely = 0.
There you choose to go! Hope we aided.
D = 0.25 sin (6.8x + 28t) a million)w(omega)=28 v=rw [right here r is amplitude] v=0.25*28=7 m/s w=2*pi*f [f=frequency] f=4.40 six Hz v=n*lambda [lambda=wavwlength] lambda=a million.fifty seven m 2)f=4.40 six Hz 3)v=7 m/s [calculated in question no a million] 4)a=0.25 5) D = 0.25 sin (6.8x + 28t) distinguishing wrt to t dD/dt=0.25*28cos(6.8x+28t) velocity is max whilst cos(6.8x+28t)=a million & min though cos(6.8x+28t) is 0 maximum v=0.25*28*a million=7 m/s min v=0.25*28*0=0