Physics, 06.01.2021 09:20 miyahvictoria
Two traveling sinusoidal waves are described by the wave functions y1 = 4.85 sin [(4.35x − 1270t)] y2 = 4.85 sin [(4.35x − 1270t − 0.250)] where x, y1, and y2 are in meters and t is in seconds. (a) What is the amplitude of the resultant wave function y1 + y2?
Answers: 2
.![y_1 = 4.85\, \sin[(4.35\, x - 1270\, t) + 0]](/tpl/images/1015/9293/3c764.png)
.![y_2 = 4.85\, \sin[(4.35\, x - 1270\, t) + (-0.250)]](/tpl/images/1015/9293/75412.png)
.
and 
share the same frequency and wavelength. The only distinction between these two waves is the 
in 
. 
would still be a sine wave. The amplitude of 
could be found without using calculus.
.
to 
and 
. Apply the sum-of-angle identity of sine to rewrite ![\begin{aligned}y_2 &= 4.85\, \sin[(\underbrace{4.35\, x - 1270\, t}_{a}) + (\underbrace{-0.250}_{b})]\\ &= 4.85 \, [\sin(4.35\, x - 1270\, t)\cdot \cos(-0.250) \\ &\quad\quad\quad\; + \cos(4.35\, x - 1270\, t)\cdot \sin(-0.250)] \end{aligned}](/tpl/images/1015/9293/2cf28.png)
.![\begin{aligned}& y_1 + y_2\\[0.5em] &= 4.85\, [\sin(4.35\, x - 1270\, t) \\ &\quad \quad \quad\;+\sin(4.35\, x - 1270\, t)\cdot \cos(-0.250) \\ &\quad\quad\quad\; + \cos(4.35\, x - 1270\, t)\cdot \sin(-0.250)] \\[0.5em] &= 4.85\, [\sin(4.35\, x - 1270\, t)\cdot (1 + \cos(-0.250)) \\ &\quad\quad\quad\; + \cos(4.35\, x - 1270\, t)\cdot \sin(-0.250)] \end{aligned}](/tpl/images/1015/9293/d46ed.png)
.
and 
that satisfy the following hypothetical equation?![\begin{aligned}& (4.85\, m)\cdot \sin((4.35\, x - 1270\, t) + c)\\&= 4.85\, [\sin(4.35\, x - 1270\, t)\cdot (1 + \cos(-0.250)) \\ &\quad\quad\quad\; + \cos(4.35\, x - 1270\, t)\cdot \sin(-0.250)] \end{aligned}](/tpl/images/1015/9293/87879.png)
.
.![\begin{aligned}& m\cdot \sin((4.35\, x - 1270\, t) + c)\\[0.5em]&=m\, \sin(4.35\, x - 1270\, t)\cdot \cos(c) \\ &\quad\quad + m\, \cos(4.35\, x - 1270\, t)\cdot \sin(c) \\[0.5em] &=\sin(4.35\, x - 1270\, t)\cdot (m\, \cos(c)) \\ &\quad\quad + \cos(4.35\, x - 1270\, t)\cdot (m\, \sin(c)) \end{aligned}](/tpl/images/1015/9293/f8914.png)
.
and 
, the following should be satisfied:
, and
.
:
.
.
.
.
.
.
.
back to the system to find 
isn't required for finding the amplitude of 
. 
radians.)
is a real number, the amplitude of 
.
.
Other questions on the subject: Physics
Physics, 22.06.2019 10:00, jonlandis6
Need people build a dam to create a reservoir that supplies water a nearby city needs. describe two ways this action will likely affect the water cycle in the local environment. (5 points) worth 20 points
Answers: 1
Physics, 22.06.2019 14:00, 6224968918
Select for each of the following statements whether it is correct or incorrect. (a) in an isothermal expansion of an ideal gas. (b) the temperature remains constant. (b) the pressure remains constant. (c) there is work done by the gas. (d) there is heat added to the gas. (e) the change in internal energy equals zero.
Answers: 1
You know the right answer?
Two traveling sinusoidal waves are described by the wave functions y1 = 4.85 sin [(4.35x − 1270t)] y...
Questions in other subjects:
Mathematics, 18.10.2020 14:01
History, 18.10.2020 14:01
Chemistry, 18.10.2020 14:01
Mathematics, 18.10.2020 14:01
French, 18.10.2020 14:01
Mathematics, 18.10.2020 14:01
Mathematics, 18.10.2020 14:01
Chemistry, 18.10.2020 14:01
