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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

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Answer:

Fossil-fueled cars are still outnumbering the alternative and replacement-fueled cars because they are generally cost-effective and are efficient.

Explanation:

<em>Fossil fuels</em> are non-renewable energy that cannot be replenished. Although many people know how harmful using them can be to the environment, still, people continue to buy cars that are powered by it. This is because, <em>using fossil-fueled cars can help you save money</em> compared to using<em> replacement-fueled cars.</em><em> Its engines are also more powerful,</em> which means they can arrive at their destination in just a few minutes. <u>This makes it efficient.</u> The cost of maintaining a fossil-fueled car is less expensive compared to<em> replacement-fueled cars.</em> People are naturally keen when it comes to budgeting, thus, many people still buy cars powered by fossil fuels.

3 0
3 years ago
(1) A positive charge +3 C is separated from another positive charge of +5 C by a distance of 7m. What is the magnitude of the e
Aneli [31]

1. The magnitude of the electric force between the two charges is 2.8×10⁹ N (Option B)

2. The net charge on the molecule is -8×10⁻¹⁹ C (Option D)

3. The magnitude of the force between the charges is 16000 N (Option C)

4. The correct statement is: A neutral object has equal numbers of protons and electrons. (Option C)

<h3>1. How to determine the force</h3>
  • Charge 1 (q₁) = +3 C
  • Charge 2 (q₂) = +5 C
  • Electric constant (K) = 9×10⁹ Nm²/C²
  • Distance apart (r) = 7 m
  • Force (F) =?

F = Kq₁q₂ / r²

F = (9×10⁹ × 3 × 5) / (7)²

F = 2.8×10⁹ N

<h3>2. How to determine the net charge on the molecule</h3>
  • Electron = 223 electrons
  • Proton = 218 protons
  • Net Charge =?

Charge = Proton - Electron

Charge = 218 - 223

Charge = -5 electrons

But

1 electron = 1.6×10⁻¹⁹ C

Thus,

Net Charge = -5 × 1.6×10⁻¹⁹ C

Net Charge = -8×10⁻¹⁹ C

<h3>3. How to determine the force</h3>
  • Charge 1 (q₁) = 2×10⁻⁴ C
  • Charge 2 (q₂) = 8×10⁻⁴ C
  • Electric constant (K) = 9×10⁹ Nm²/C²
  • Distance apart (r) = 0.3 m
  • Force (F) =?

F = Kq₁q₂ / r²

F = (9×10⁹ × 2×10⁻⁴ × 8×10⁻⁴) / (0.3)²

F = 16000 N

<h3>4. What is a neutral object?</h3>

A neutral object is an object having equal numbers of protons and electrons. For example, an object with 4 protons and 4 electrons is said to be neutral as illustrated below

  • Electron = 4 electrons
  • Proton = 4 protons
  • Net Charge =?

Charge = Proton - Electron

Charge = 4 - 4

Charge = 0 (neutral)

Thus, the correct statement about neutral object, given in the question is: A neutral object has equal numbers of protons and electrons (Option C)

Learn more about Coulomb's law:

brainly.com/question/506926

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2 years ago
HELP ASAP<br> WHAT ARE PROPERTIES OF WATER
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You used the right-hand rule to determine the z component of the angular momentum, but as a check, calculate in terms of positio
KengaRu [80]

Answer:

case x py   L is in the positive z direction

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Explanation:

The angular amount is defined by the relation

         L = r x p

the bold are vectors, where r is the position vector and p is the linear amount vector.

The module of this vector can be concentrated by the relation

         L = r p sin θ

the direction of the vector L can be found by the right-hand rule where the thumb points in the direction of the displacement vector, the fingers extended in the direction of the moment p which is the same direction of speed and the palm points in the direction of the angular momentum L

in the case x py

the thumb is in the x direction, the fingers are extended in the direction and the palm is in the positive z direction

In the case y px

the thumb is in the y direction, the fingers are in the x direction, the palm is in the negative z direction

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A girl is floating in a freshwater lake with her head just above the water. If she weighs 610 N, what is the volume of the subme
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Answer:

The volume of the submerged part of her body is 0.0622m^{3}

Explanation:

Let's define the buoyant force acting on a submerged object.

In a submerged object acts a buoyant force which can be calculated as :

B=ρ.V.g

Where ''B'' is the buoyant force

Where ''ρ'' is the density of the fluid

Where ''V'' is the submerged volume of the object

Where ''g'' is the acceleration due to gravity

Because the girl is floating we can state that the weight of the girl is equal to the buoyant force.

We can write :

W_{girl}=B (I)

Where ''W'' is weight

⇒ If we consider ρ = 1000\frac{kg}{m^{3}} (water density) and g=9.81\frac{m}{s^{2}} and replacing this values in the equation (I) ⇒

B=W_{girl}

B=610N

ρ.V.g = 610N

1000\frac{kg}{m^{3}}.V.(9.81\frac{m}{s^{2}})=610N (II)

The force unit ''N'' (Newton) is defined as

N=kg.\frac{m}{s^{2}}

Using this in the equation (II) :

(9810\frac{N}{m^{3}}).V =610N

V=\frac{610N}{9810\frac{N}{m^{3}}}

V=0.0622m^{3}

We find that the volume of the submerged part of her body is 0.0622m^{3}

8 0
3 years ago
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