PHYSICS COLLEGE

To see how two traveling waves of the same frequency create a standing wave. Consider a traveling wave described by the formula y1(x,t)=Asin(kx−ωt)
This function might represent the lateral displacement of a string, a local electric field, the position of the surface of a body of water, or any of a number of other physical manifestations of waves.
1. Find ye(x) and yt(t). Keep in mind that yt(t) should be a trigonometric function of unit amplitude.
2. At the position x=0, what is the displacement of the string (assuming that the standing wave ys(x,t) is present)?
3. At certain times, the string will be perfectly straight. Find the first time t1>0 when this is true.
4. Which one of the following statements about the wave described in the problem introduction is correct?
A. The wave is traveling in the +x direction.
B. The wave is traveling in the −x direction.
C. The wave is oscillating but not traveling.
D. The wave is traveling but not oscillating.
Which of the expressions given is a mathematical expression for a wave of the same amplitude that is traveling in the opposite direction? At time t=0this new wave should have the same displacement as y1(x,t), the wave described in the problem introduction.
A. Acos(kx−ωt)
B. Acos(kx+ωt)
C. Asin(kx−ωt)
D. Asin(kx+ωt)

Answers

Answer 1

Answer:

The definition of standing wave and trigonometry allows to find the results for the questions about the waves are:

1. For the standing wave its parts are: spatial $y_e = A' \ sin \ kx$ and

temporal part $y_t = A' \ cos \ wt$

2. The string moves with an oscillating motion y = A’ cos wt.

3. Thefirst displacement is zero for $t = (\pi )/(2w)$

4. the correct result is:

A. The wave is traveling in the +x direction.

5. The correct result is:

D. Asin(kx+ωt)

Traveling waves are periodic movements of the media that transport energy, but not matter, the expression to describe it is:

y₁ = A sin (kx -wt)

Where A is the amplitude of the wave k the wave vector, w the angular velocity and x the position and t the time.

1. Ask us to find the spatial and temporal part of the standing wave.

To form the standing wave, two waves must be added, the reflected wave is:

y₂ = A sin (kx + wt)

The sum of a waves

y = y₁ + y₂

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

We develop the sine function and add.

Sin (a ± b) = sin a cos b ± sin b cos a

The result is:

y = 2A sin kx cos wt

They ask that the function be unitary therefore

The amplitude of each string

A_ {chord} = A_ {standing wave} / 2

The spatial part is

$y_e$ = A 'sin kx

The temporary part is:

$y_t$ = A ’cos wt

2. At position x = 0, what is the displacement of the string?

y = A ’cos wt

The string moves in an oscillating motion.

3. At what point the string is straight.

When the string is straight its displacement is zero x = 0, the position remains.

y = A ’cos wt

For the amplitude of the chord to be zero, the cosine function must be zero.

wt = (2n + 1) $(\pi)/(2)$

the first zero occurs for n = 0

wt = $(\pi )/(2)$

t = $(\pi )/(2w)$

4) The traveling wave described in the statement is traveling in the positive direction of the x axis, therefore the correct statement is:

A. The wave is traveling in the +x direction.

5) The wave traveling in the opposite direction is

y₂ = A sin (kx + wt)

The correct answer is:

D. Asin(kx+ωt)

In conclusion using the definition of standing wave and trigonometry we can find the results for the questions about the waves are:

1. For the standing wave its parts are: spatial $y_e = A' \ sin \ kx$ and

temporal part $y_t = A' \ cos \ wt$

2. The string moves with an oscillating motion y = A’ cos wt.

3. Thefirst displacement is zero for $t = (\pi )/(2w)$

4. the correct result is:

A. The wave is traveling in the +x direction.

5. The correct result is:

D. Asin(kx+ωt)

Learn more about standing waves here: brainly.com/question/1121886

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A lead ball is dropped into a lake from a diving board 5.0 m above the water. After entering the water, it sinks to the bottom with a constant velocity equal to the velocity with which it hit the water. The ball reaches the bottom 3.0 s after it is released. How deep is the lake

Answers

Answer:

$|D_(depth) |=19.697m$

Explanation:

To find Depth D of lake we must need to find the time taken to hit the water.So we use equation of simple motion as:

Δx=vit+(1/2)at²

$x_(f)-x_(i)=v_(i)t+(1/2)at^(2)\n -5.0m=(o)t+(1/2)(-9.8m/s^(2) )t^(2)\n -4.9t^(2)=-5.0\n t^(2)=5/4.9\nt=√(1.02) \nt=1.01s$

As we have find the time taken now we need to find the final velocity vf from below equation as

$v_(f)=v_(i)+at\nv_(f)=0+(-9.8m/s^(2) )(1.01s) \nv_(f)=-9.898m/s$

So the depth of lake is given by:

first we need to find total time as

t=3.0-1.01 =1.99 s

$|D_(depth) |=|vt|\n|D_(depth) |=|(-9.898m/s)(1.99s)|\n|D_(depth) |=19.697m$

Observer 1 rides in a car and drops a ball from rest straight downward, relative to the interior of the car. The car moves horizontally with a constant speed of 3.80 m/s relative to observer 2 standing on the sidewalk.a) What is the speed of the ball 1.00 s after it is released, as measured by observer 2?

b) What is the direction of travel of the ball 1.00 s after it is released, as measured relative to the horizontal by observer 2?

Answers

a) 10.5 m/s

While for observer 1, in motion with the car, the ball falls down straight vertically, according to observer 2, which is at rest, the ball is also moving with a horizontal speed of:

$v_x = 3.80 m/s$

As the ball falls down, it also gains speed along the vertical direction (due to the effect of gravity). The vertical speed is given by

$v_y = u_y + gt$

where

$u_y =0$ is the initial vertical speed

g = 9.8 m/s^2 is the acceleration of gravity

t is the time

Therefore, after t = 1.00 s, the vertical speed is

$v_y = 0 + (9.8)(1.00)=9.8 m/s$

And so the speed of the ball, as observed by observer 2 at rest, is given by the resultant of the horizontal and vertical speed:

$v=√(v_x^2 +v_y^2)=√((3.8)^2+(9.8)^2)=10.5 m/s$

b) $\theta = -68.8^(\circ)$

As we discussed in previous part, according to observer 2 the ball is travelling both horizontally and vertically.

The direction of travel of the ball, according to observer 2, is given by

$\theta = tan^(-1) ((v_y)/(v_x))=tan^(-1) ((-9.8)/(3.8))=-68.8^(\circ)$

We have to understand in which direction is this angle measured. In fact, the car is moving forward, so $v_x$ has forward direction (we can say it is positive if we take forward as positive direction).

Also, the ball is moving downward, so $v_y$ is negative (assuming upward is the positive direction). This means that the direction of the ball is forward-downward, so the angle above is measured as angle below the positive horizontal direction:

$\theta = -68.8^(\circ)$

Explain why it is dangerous to jump from a fast moving train

Answers

Answer:

When you jump off a train, you jump off a certain height and your downwards (vertical) velocity is zero. But your forward (horizontal) velocity is not. You will hit the ground on split second with your horizontal velocity practically the same as the train.

Explanation:

you be in serious injury.

What was the main idea of Malthus theory of population

Answers

Answer:

The idea that population growth is potentially exponential while the growth of the food supply or other resources is linear.

Explanation:

Consider a bird that flies at an average speed of 10.7 m/s and releases energy from its body fat reserves at an average rate of 3.70 W (this rate represents the power consumption of the bird). Assume that the bird consumes 4.00g of fat to fly over a distance db without stopping for feeding. How far will the bird fly before feeding again?Fat is a good form of energy storage because it provides the most energy per unit mass: 1.00 grams of fat provides about 9.40 (food) Calories, compared to 4.20 (food) Calories per 1.00 grams of carbohydrate. Remember that Calories associated with food, which are always capitalized, are not exactly the same as calories used in physics or chemistry, even though they have the same name. More specifically, one food Calorie is equal to 1000 calories of mechanical work or 4186 joules. Therefore, in this problem use the conversion factor 1Cal=4186J.