1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
timofeeve [1]
3 years ago
7

Two transverse waves travel along the same taut string inopposite directions. the waves are described by following equations use

superposition to determine the standing wave function
Physics
1 answer:
Umnica [9.8K]3 years ago
4 0

Answer: y'=2Asin(kx)cos(wt)

Explanation:

Let y1=A sin (kx + wt) be the first wave

y2=A sin (kx - wt) be the second wave in the opposite direction (which we showed by putting a negative sign between the terms kx and wt)

Please do note that both wave have the same attributes (that's Amplitude, wave number and angular frequency) because they are formed on the same medium by the same source just that their directions are opposite.

By super imposing these 2 waves, we have a resulting singular wave representing both wave (law of superimposition) with a resulting value of vertical displacement y'.

Thus y' = y1 + y2.

Let us do the math.

y'=A sin (kx + wt) + A sin (kx - wt)

By factoring A out, we have that

y' = A [ sin (kx + wt) + sin (kx - wt)]

For simplicity let us use the substitution

Let (kx + wt) = a and (kx - wt) =b

Hence we have that

y' = A [sin a + sin b].

From trigonometric ratio

sin a + sin b = 2sin[(a+b)/2] * cos [(a - b)/2]

By recalling that (kx + wt) = a and (kx - wt) =b

sin a + sin b = 2sin [(kx +wt +kx-wt) /2] * cos [(kx +wt - (kx-wt))/2]

Thus we have that

sin a + sin b = 2sin [(kx+wt+kx-wt)/2] * cos[(kx+wt-kx+wt)/2]

By collecting like terms in the bracket we have that

sin a + sin b = 2sin[2kx/2] * cos [2wt/2]

By dividing

sin a + sin b = 2sin(kx) cos(wt)

Now let us get the final resultant vertical displacement (y')

Recall that

y' = A [sin a + sin b]. and we already deduced that

sin a + sin b = 2sin(kx) cos(wt)

Finally,

y' = A [2sin(kx) cos(wt)] which is

y'=2Asin(kx)cos(wt)...... Final answer

You might be interested in
Suppose you are walking in an airliner in flight. Use Newton’s third law to describe the effect of your walk on the motion on th
Novosadov [1.4K]

Answer:

The effect of your walking will create a force on the airline acting downwards, due to the weight. By Newton's thirds law the airline will exert an equal and opposite reaction force directed downwards.

Explanation:

The weight of all the passengers acts downwards on the floor of the Airplane.

The Airplane exerts an equal and opposite force on the passengers, with the help of its propulsion due to which the flight keeps on flying without falling down.

Hence by changing the frame of reference we can observe the force which is responsible for the reaction.

4 0
2 years ago
How many light sources do you know <br> Pls list them
Alex73 [517]
The sun is the primary source of light. Other artificial sources are light bulb, torch light and some others. Thats all i can think of.
8 0
3 years ago
Read 2 more answers
A soccer ball is kicked and left
Vedmedyk [2.9K]

Answer:

Explanation:

Considering that this is parabolic motion, we know that the time the ball is in the air begins the instant it leaves the ground, reaches up to its max height, and then begins falling until it reaches the ground. Duh, right? Some important things happen during this trip. There are a few things we need to know in order to even begin the problem. Parabolic motion has x and y coordinates because it is 2-dimmensional; the acceleration in the x dimension is not the same as the acceleration in the y dimension; the velocity of an object at its max height is always 0; the time it takes to reach its max height (where the max height is half the distance the object travels) is half the time it takes to make the whole trip. Yikes. That's a lot to know and much to remember! Don't you just LOVE physics!?

For a. the hang time is the time the ball was in the air. Some of that stuff we talked about above is pertinent to solving this problem. We know that the velocity of the ball is 0 at its max height, and we also know that if we find the time it takes to reach its max height, we can double that number to find how long it was in the air for the whole trip. Use the one-dimensional equation

v=v_0+at to find out how long it took to reach the max height. Even though we don't yet know the max height, we DO know that the velocity at that point is 0. BUT before we do that, since we are working in the y-dimension only, it would behoove us (benefit us) to find the velocity particular to this dimension. We are going to answer c. first, then backtrack.

c. wants the initial vertical velocity. That is found in the magnitude of the "blanket" or generic velocity times the sin of the angle, namely:

V_y=25sin(45) so

V_y= 18 m/s Now we can use that as the initial upwards velocity in part a:

v=v_0+at and filling in:

0 = 18 + (-9.8)t and

-18 = -9.8t so

t = 1.8 seconds. But remember, this is only half the time it was in the air. The whole trip, then, takes 2(1.8) which is

t = 3.6 seconds

That's a and c. Now for b:

b. asks for the x component of the velocity:

V_x=Vcos\theta which works out to be the same as the vertical velocity, since the sin and cos of 45 degrees is the same:

V_x=25cos45 and

V_x= 18 m/s

Onto d:

d. wants the max height. Remember, it took 1.8 seconds to get to the max height, so using yet another one-dimensional equation:

Δx = v₀t + \frac{1}{2}at^2 where Δx is the displacement, v₀ is the initial upwards velocity, a is the pull of gravity, and t is the time it takes to reach that max height (Δx, our unknown). Filling in:

Δx = 18(1.8)+\frac{1}{2}(-9.8)(1.8)^2 and if you do the rounding correctly, you'll end up with this:

Δx = 32 - 16 so

the max height, Δx, is 16 meters.

e. wants the range. That translates to the distance the ball traveled. This is found in a glorified version of d = rt, where d is displacement, r is velocity, and t is...well, time (that doesn't change):

Δx = vt so

Δx = 18(3.6) remember that the ball was in the air for a total of 3.6 seconds, so

Δx = 65 meters.

Phew!!!!! That's a lot! I suggest you learn your physics or this will make you insane by the end of the course!

6 0
3 years ago
Lou’s pet parrot looks as through it has many more features on cold days than it appears to have on warm ones. Loy determines th
Alexus [3.1K]

it has many more features on cold days than it appears to have on warm ones; thats the independant variable i believe

8 0
3 years ago
A box of mass 0.8 kg is placed on an inclined surface that makes an angle 30 above
earnstyle [38]

Answer:

a)    a = 17.1 m / s², b)    F = 3.04 N

Explanation:

This is an exercise of Newton's second law, in this case the selection of the reference system is very important, we have two possibilities

* a reference system with the horizontal x axis, for this selection the normal and the friction force have x and y components

* a reference system with the x axis parallel to the plane, in this case the weight and the applied force have x and y components

We are going to select the second possibility, since it is the most used in inclined plane problems, let's analyze the angle of the applied force (F) it has an angle 10º with respect to the x axis, if we rotate this axis 30º the new angle is

                θ = 10 -30 = -20º

The negative sign indicates that it is in the fourth quadrant. Let's use trigonometry to find the components of the applied force

              sin (-20) = F_{y} / F

              cos (-20) = Fₓ / F

              F_{y} = F sin (-20)

              Fₓ = F cos (-20)

              F_y = 18 sin (-20) = -6.16 N

              Fₓ = 18 cos (-20) = 16.9 N

The decomposition of the weight is the customary

               sin 30 = Wₓ / W

               cos 30 = W_y / W

               Wₓ = W sin 30 = mg sin 30

                W_y = W cos 30 = m g cos 30

                Wₓ = 0.8 9.8 sin 30 = 3.92 N

                 W_y = 0.8 9.8 cos 30 = 6.79 N

Notice that in the case  the angle is measured with respect to the axis y perpendicular to the plane

Now we can write Newton's second law for each axis

X axis

      Fₓ - fr = m a

Y Axis  

      N - F_{y} - Wy = 0

      N =F_{y} + Wy

      N = 6.16 + 6.79

     

They both go to the negative side of the axis and

      N = 12.95 N

The friction force has the formula

        fr = μ N

we substitute

        Fₓ - μ N = m a

        a = (Fₓ - μ N) / m

     

we calculate

       a = (16.9 - 0.25 12.95) / 0.8

       a = 17.1 m / s²

b) now the block slides down with constant speed, therefore the acceleration is zero

ask for the value of the applied force, we will suppose that with the same angle, that is, only its modulus was reduced

       Newton's law for the x axis

              Fₓ -fr = 0

              Fₓ = fr

              F cos 20 = μ N

              F = μ N / cos 20

we calculate

              F = 0.25 12.95 / cos 20

              F = 3.04 N

this is the force applied at an angle of 10º to the horizontal

3 0
3 years ago
Other questions:
  • With what initial velocity must an object be thrown upward from a height of 2 meters to reach a maximum hieght of 200 meters
    10·1 answer
  • Olivia wants to find out whether a substance will fluoresce. She says she should put it in a microwave oven. Do you agree with h
    12·2 answers
  • As the air on the surface of the earth warms what happens to the density of the air
    7·1 answer
  • What is meant by the statement that you don’t “own” the atoms that make up your body?
    6·1 answer
  • 9. The three types of stress that act on Earth's rocks are compression, tension, and A. strain. B. shear. C. tephra. D. shale.
    13·2 answers
  • PLS ANSWER FAST WILL GIVE BRAINLY!!!! ANSWER ONLY IF YOU KNOW!!!!
    10·1 answer
  • A drop of oil of volume 10m it spread out on water to make a circular firm of radius 10m calculate the tickness of the firm
    15·1 answer
  • Need help ASAP please Thanks
    5·1 answer
  • The purpose of a cell phone cover is to protect your phone from impact forces. How does a cell phone case do this?
    8·1 answer
  • What is a work out time setting? (Gym)
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!