Answer:
The wavelength is ![\lambda = 0.01367 m](https://tex.z-dn.net/?f=%5Clambda%20%20%3D%20%200.01367%20m)
The wave number is ![N = 73.18\ m^{-1}](https://tex.z-dn.net/?f=N%20%3D%2073.18%5C%20m%5E%7B-1%7D)
The wave function is ![y= 1.57 *10^{-6} sin 2 \pi ( 73.178 x -25100t)](https://tex.z-dn.net/?f=y%3D%201.57%20%2A10%5E%7B-6%7D%20sin%202%20%5Cpi%20%28%2073.178%20x%20-25100t%29)
Explanation:
From the question we are told that
The frequency of the sound wave is ![f = 25,100 Hz](https://tex.z-dn.net/?f=f%20%3D%20%2025%2C100%20Hz)
The speed of the wave is ![v = 343 m/s](https://tex.z-dn.net/?f=v%20%20%3D%20%20343%20m%2Fs)
The wavelength of the wave is mathematically evaluated as
![\lambda = \frac{v}{f}](https://tex.z-dn.net/?f=%5Clambda%20%20%3D%20%20%5Cfrac%7Bv%7D%7Bf%7D)
substituting values
![\lambda = \frac{343}{25100}](https://tex.z-dn.net/?f=%5Clambda%20%20%3D%20%20%5Cfrac%7B343%7D%7B25100%7D)
![\lambda = 0.01367 m](https://tex.z-dn.net/?f=%5Clambda%20%20%3D%20%200.01367%20m)
The wave number is mathematically represented as
![N= \frac{1}{\lambda }](https://tex.z-dn.net/?f=N%3D%20%20%5Cfrac%7B1%7D%7B%5Clambda%20%7D)
substituting values
![N = \frac{1}{ 0.01367 }](https://tex.z-dn.net/?f=N%20%20%3D%20%20%5Cfrac%7B1%7D%7B%200.01367%20%7D)
![N = 73.18\ m^{-1}](https://tex.z-dn.net/?f=N%20%3D%2073.18%5C%20m%5E%7B-1%7D)
The general form of wave function is
![y= A sin (kx -wt)](https://tex.z-dn.net/?f=y%3D%20A%20%20sin%20%28kx%20-wt%29)
given that the amplitude is ![A = 1.57*10^{-6} \ m](https://tex.z-dn.net/?f=A%20%3D%20%201.57%2A10%5E%7B-6%7D%20%5C%20m)
While
which is the angular velocity is represented as ![w = 2 \pi f](https://tex.z-dn.net/?f=w%20%3D%20%202%20%5Cpi%20f)
and k which is the angular wave number is mathematically represented as ![k = \frac{2 \pi }{\lambda }](https://tex.z-dn.net/?f=k%20%20%3D%20%20%5Cfrac%7B2%20%5Cpi%20%7D%7B%5Clambda%20%7D)
The wave function becomes
![y= A sin 2 \pi (\frac{1}{\lambda} x -ft)](https://tex.z-dn.net/?f=y%3D%20A%20%20sin%202%20%5Cpi%20%28%5Cfrac%7B1%7D%7B%5Clambda%7D%20x%20-ft%29)
substituting values
![y= 1.57 *10^{-6} sin 2 \pi ( 73.178 x -25100t)](https://tex.z-dn.net/?f=y%3D%201.57%20%2A10%5E%7B-6%7D%20sin%202%20%5Cpi%20%28%2073.178%20x%20-25100t%29)
Answer:
V = E * d voltage equals charge on plates * separation
F = E q force on charge q equals electric field * charge
W = F * d work done equals force times the distance moved
From the very first equation, the voltage depends on the distance between the plates - while the electric field remains constant
The <u>potential difference will decrease</u> as the separation of the plates increases because W remains constant - work done in moving test charge from one plate to another is constant - voltage is constant
given that :
UA=15i+30j and UB =-10+5.0j
speed before collision is given as
u₁ = sqrt(15² + 30²) = 33.5 m/s
and
u₂ = sqrt((- 10)² + 5²) = 11.2 m/s
total kinetic energy before collision is given as
KE = (0.5) m u²₁ + (0.5) m u²₂ = (0.5) (2) (33.5)² + (0.5) (2) (11.2)² = 1247.7 J
similarly final speed after collision is given as
v₁ = sqrt((- 5)² + (20)²) = 20.6 m/s
v₂ = sqrt((10)² + (15)²) = 18 m/s
total kinetic energy after collision is given as
KE' = (0.5) m v²₁ + (0.5) m v²₂ = (0.5) (2) (20.6)² + (0.5) (2) (18)² = 748.4 J
Change in kinetic energy is given as
ΔKE = KE' - KE
inserting the values
ΔKE = 748.4 - 1247.7
ΔKE = - 499.3 J
hence kinetic energy lost comes out to be 499.3 J
<span>Brake </span>is not included in your
perception time.
<span>To add, the total stopping distance of a vehicle is made up
of 4 components. The human </span>perception time; is how long the driver<span> takes to see the hazard, and the brain realize
it is a hazard requiring an immediate reaction.</span>