Answer:
At 23.5 deg north of the equator this person would see the sun directly overhead at the summer solstice at noon
When riding on a bus, you can tell you are moving by
observing the motion of objects like other moving vehicles
outside the window.
True or False?
Answer:
True
Explanation:
a heavy crate rests on the bed of a flatbed truck. when the truck accelerates, the crate remains where it is on the truck so it too accelerates. what force(s) is/are responsible for the acceleration of the crate? be specific as to the root causes (on, by) of this force.
The force responsible for the acceleration of the crate is the frictional force between the crate and the bed of the truck.
When the truck accelerates, the crate tends to remain at rest due to inertia. However, the frictional force between the crate and the bed of the truck acts in the forward direction, allowing the crate to accelerate along with the truck.
This frictional force is a result of the interaction between the surfaces of the crate and the truck bed. Without this frictional force, the crate would slide or move independently from the truck's acceleration.
The frictional force arises due to the microscopically rough surfaces of the crate and the truck bed. As the two surfaces are pressed against each other, intermolecular forces come into play, resulting in the generation of the frictional force
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A 3.0-kg ball with an initial velocity of (4.0i + 3.0j) m/s collides with a wall and rebounds with a
velocity of (-4.0i + 3.0j) m/s. what is the impulse exerted on the ball by the wall?
The impulse exerted on the ball by the wall is 24i kgm/s.
Impulse exerted by the ball on the wall
The impulse exerted by the ball on the wall is the change in the linear momentum of the ball.
J = ΔP
ΔP = Pf - Pi
P = mv
where;
m is mass of the ballv is the velocityΔP = 3(4.0i + 3.0j) - 3(-4.0i + 3.0j)
ΔP = (12i + 9j) - (-12i - 9j)
ΔP = 24i kgm/s
Thus, the impulse exerted on the ball by the wall is 24i kgm/s.
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What is the length of the x-component of the vector shown below?
The length of the x-component of the vector is approximately 48.55 units.
What is the length of the x-component of the vector?To find the length of the x-component of the vector, we need to use trigonometry.
We can use the angle and the magnitude (length) of the vector to find the x-component using the formula:
x-component = magnitude x cos(angle)
Plugging in the values given, we get:
x-component = 52 units x cos(21⁰)
x-component = 52 units x 0.9336
Multiplying these two numbers, we get:
x-component ≈ 48.55 units
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two step dimensional analysis
(step by step)
convert :
4900mm to cm
5.59kL to quarts
When we convert 4900mm from two-step dimensional analysis it would be 490 cm and 5.59kL to 5923.667 quarts.
What is dimensional Analysis?Dimensional Analysis is a technique for analysis where physical quantities are expressed in terms of their basic dimensions and is frequently applied when there is insufficient data to create accurate equations.
As given in the problem we have to convert
4900mm to cm
As we know that there are 1000 mm in 1 m
1000 mm = 1 m
4900 mm = 4.9 m
1 m = 100 cm
4.9 m = 4.9×100
=490 cm
As we have to convert 5.59kL to quarts
1 Kiloliter = 1056.69 US liquid quart
5.59kL = 5.59 ×1056.69 quarts
=5923.667 quarts
Thus, we converted 4900mm to 490 cm and 5.59kL to 5923.667 quarts.
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Earthquake waves are 35m long and arrive at a frequency of 2.0Hz. How fast are they travelling?
Answer:
70 m/s
Explanation:
The frequency of earthquake = 2.0 Hz
The wavelength = 35 m
How fastbthw earthquake is t traveling is given bythw velocity of the wave, velocity of wave is related to frequency and wavelength using the formula :
V = frequency * wavelength
V = 2 * 35
V = 70 m/s
The thermal energy of 0.700 mol of a substance is increased by 0.800 J. (A) What is the temperature change if the system is a monatomic gas?
If it's a monatomic gas system the difference in temperature is about 0.212 K.
What element has monatomic gases in it?Helium, neon, argon, krypton, radon, xenon, and neon are a few examples of monatomic gases (the noble gases).
The following equation can be used to determine the temperature change for a monatomic gas:
U is calculated using the formula U = (3/2) * n * R * T, where n is the number of moles, R is the gas constant, and T is the temperature.
To solve for T, rewrite the problem as follows:
T = (2/3) * U / (n * R)
We may now change the values provided:
T = (0.700 mol * 8.31 J/mol K) * (2/3) * 0.800 J
T = 0.212 K
Thus, the difference in temperature is almost 0.212 K.
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If each component has a plate contact surface area of 1 cm2 and the corresponding contact resistance is 2 104 m2 K/W, what is the component temperature
(a) To determine the temperature of the copper plate, we can use the formula:
Q = m_dot x Cp x (T_out - T_in)
where Q is the heat transfer rate, m_dot is the mass flow rate of water, Cp is the specific heat capacity of water, and T_out and T_in are the outlet and inlet temperatures of the water, respectively.
The heat transfer rate can be calculated as:
Q = 100 x 25 W = 2500 W
The mass flow rate of water can be calculated as:
m_dot = rho x V x A
where rho is the density of water, V is the velocity of water, and A is the area of the plate.
rho = 1000 kg/m³ (density of water)
V = 2 m/s (given)
A = 0.2 m x 0.2 m = 0.04 m² (area of the plate)
Therefore, m_dot = 1000 kg/m³x 2 m/s x 0.04 m² = 80 kg/s
The specific heat capacity of water is Cp = 4186 J/kg-K.The outlet temperature of the water is given as T_out = 17°C = 290 K (approx).
Assuming the copper plate is isothermal, we can equate the heat transfer rate to the thermal energy generated by the components:
Q = 100 x P
where P is the power dissipation per component.
Therefore, P = Q/100 = 25 W
The contact resistance between the component and the copper plate is given as 2 x 10⁴ m² K/W. The contact area between each component and the copper plate is 1 cm²= 0.0001 m².
Using the formula for the thermal resistance of a component:
R_th = 1/(h x A_c)
where h is the heat transfer coefficient and A_c is the contact area, we can calculate the value of h:
R_th = 2 x 10⁴m² K/W
A_c = 0.0001 m²
Therefore, h = 1/(R_th x A_c) = 5000 W/m² K
Assuming the components are at a uniform temperature, we can use the formula for convection heat transfer to calculate the component temperature:
P = h x A_c x (T_plate - T_comp)
where T_comp is the component temperature.
Rearranging the formula, we get:
T_comp = T_plate - (P/(h x A_c))
The temperature of the copper plate is approximately 82.3°C, which can be calculated using the first formula.
Plugging in the values, we get:
Q = 80 kg/s x 4186 J/kg-K x (290 K - T_plate)
Solving for T_plate, we get:
T_plate = 82.3°C
(b) The component temperature can be calculated using the second formula:
T_comp = T_plate - (P/(h x A_c))
Plugging in the values, we get:
T_comp = 82.3°C - (25 W/(5000 W/m² K x 0.0001 m²)) = 57.3°C
Therefore, the temperature of each component is approximately 57.3°C.
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Complete Question
One hundred electrical components, each dissipating 25 W, are attached to one surface of a square (0.2 m × 0.2 m) copper plate, and all the dissipated energy is transferred to water in parallel flow over the opposite surface. A protuberance at the leading edge of the plate acts to trip the boundary layer, and the plate itself may be assumed to be isothermal. The water velocity and temperature are "-= 2 m/s and T-= 17°C, and the water's thermophys- ical properties may be approximated as V 0.96 x 10- m2/s, k-0.620 W/m-K, and Pr-5.2. Copper plate, T, Contact area, Ac and Water resistance, Rin UUUUUUUUUUT?: Boundary ayer trip , L= 0.2 m (a) What is the temperature of the copper plate? (b) If each component has a plate contact surface area 1 cm2 and the corresponding contact resistance is 2 x 104m2. K/W, what is the component tempera- ture? Neglect the temperature variation across the thickness of the copper plate. of
Sinuosoids on the plane have four basic features: amplitude, period, phase shift (sometimes called horizontal shift), and vertical shift (sometimes represented by the equation of the sinusoid's midline). Below is the graph of a particular sinusoid which is the graph of the function f(x). (Cilick on a graph to eniarge it) Using the graph, determine the amplitude, period, phase shift and midline for the above f(x).. Note, phase shift is sometimes called horizontal shift. Also, the midline should be written as an equation not just a numerical value. Amplitude Period Phase shift Midline Using the trig function sin(x), find an equation for the graph of f(x).. For example, y=5sin(6x−7)+22.
The amplitude of the function is 5/2Period. The phase shift is Phase shift is π/2Midline and the midline of the given function f(x) is Midline = 2Using the trig function sin(x), the equation for the graph of f(x) can be written as:f(x) = (5/2) sin (x - π/2) + 2
The amplitude, period, phase shift and midline of the given function f(x) is given below:
The given sinusoidal function oscillates between -5 and 5, which is a distance of 5 from the center line.
The amplitude is half of the distance between the minimum and maximum values, which is 5/2.
Hence the amplitude of the function is = 5/2Period:
The distance between the peaks on the graph of the given sinusoidal function is 4.
Hence the period of the function is Period = 4Phase shift:
The standard position of the graph of sin(x) is y = sin(x) where the graph passes through the origin (0,0).
The given function is also sin(x) shifted to the right by π/2 units.
Hence the phase shift is Phase shift = π/2Midline:
The midline is the average value of the function. For the sine function, the midline is y = 0.
The midline of the given function f(x) is Midline = 2Using the trig function sin(x), the equation for the graph of f(x) can be written as :f(x) = (5/2) sin (x - π/2) + 2
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What is significant about the temperature 0 K
A. Matter no longer exists
B. Ice melts
C. Water freezes
D. Particles no longer move
Answer: I's either A. Matter no longer exists or D. Particles no longer move
Explanation:
Sorry if I get it wrong
Hope his helps :)
Answer:
d
Explanation:
when total internal reflection happens at a plastic-air interface:
a) half the light is refracted
b) half the light is reflected
c) light hits the interface from the air side
d) light hits the interface from the plastic side
e) the law of reflection ceases to hold
When total internal reflection happens at a plastic-air interface, light hits the interface from the plastic side. The correct answer is Option D.
Total internal reflection is a phenomenon that happens when a light ray tries to pass from a medium of high refractive index to another medium with a low refractive index. When the angle of incidence becomes greater than the critical angle of the interface, the light rays are refracted and stay inside the medium of high refractive index. If the angle of incidence is even greater, the light is reflected back into the same medium as it was coming from.
In the case of total internal reflection, the incident angle is greater than the critical angle, so the light is reflected back. The total internal reflection only occurs when the light goes from a medium with a higher refractive index to a medium with a lower refractive index.
The law of reflection holds for total internal reflection. When a ray of light hits a plastic-air interface from the plastic side with an angle of incidence greater than the critical angle, then total internal reflection occurs. Therefore, the correct option is "d) light hits the interface from the plastic side."
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atom has a central __________ surrounded by _____ . 2)Protons and neutrons are inside the _______ 3)Protons are _______ charged particles and electrons are ______ charged particles. 4)charge of neutron is _____ 5)An atom consists of equal number of __________ and __________ 6)A ___________ is a charge storing device
Answer:
1. nucleus and electron
2. nucleus
3. Positively charged, negatively charged
4. zero
5. protons and electrons
6. Capacitor
Explanation:
1. nucleus and electron - Nucleus is the central part of atom which is positively charged
2. nucleus
3. Positively charged, negatively charged - Proton have +1 change and electron have -1 charge
4. zero - Neutrons are neutral in nature and hence have no charge
5. protons and electrons
6. Capacitor
The force of gravity between these pairs of objects:a 1-kg mass and 2-kg mass that are 1 m apart;
The force of gravity between the two objects is 1.33 x 10⁻¹⁰ N.
What is the force of gravity between the two objects?
The force of gravity between the two objects is calculated by applying Newton's law of universal gravitation.
Fg = Gm₁m₂ / r²
where;
G is universal gravitation constantm₁ is mass of first objectm₂ is mass of second objectr is the distance between themFg = ( 6.67 x 10⁻¹¹ x 1 kg x 2 kg ) / ( 1 m )²
Fg = 1.33 x 10⁻¹⁰ N
Thus, the force of gravity is proportional to the product of the masses and inversely proportional to the square of the distance between them.
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White light, consisting of many wavelengths is known as --- where as light consisting of one wavelength is known as:____
White light, consisting of many wavelengths, is known as "polychromatic light," whereas light consisting of one wavelength is known as "monochromatic light."
White light is composed of a range of wavelengths spanning the visible spectrum. When white light passes through a prism or a diffraction grating, it gets separated into different colors, such as red, orange, yellow, green, blue, indigo, and violet. Each of these colors corresponds to a specific wavelength within the visible spectrum.
Polychromatic light refers to light that consists of multiple wavelengths. In the case of white light, it contains a combination of all the visible wavelengths, resulting in the perception of "white" when observed together.
On the other hand, monochromatic light refers to light that consists of only a single wavelength. It is a pure and specific color of light without any mixture of other wavelengths. Examples of monochromatic light sources include lasers, which emit light at a specific wavelength, such as red, green, or blue.
The distinction between polychromatic and monochromatic light is based on the composition of wavelengths present. Polychromatic light contains a broad spectrum of wavelengths, while monochromatic light consists of a single wavelength.
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Isaac Newton's first law of motion states?
Answer:
His first law states that every object will remain at rest or in uniform motion in a straight line unless compelled to change its state by the action of an external force. In other words its inertia.
Explanation:
Newtons first law of motion states that"A body will continue to its state of rest or motion unless external force acted upon it.
1.
You just earned a $1000 bonus at your job. Would you rather receive all the money at the end of the
year or half the money now and half the money later? Why?
PLEASE HELP!!! GIVING BRAINLIEST!! ill also answer questions that you have posted if you answer these correctly!!!! (40pts)
Answer:
Bernoulli is A
Archimedes is B
Pascal is C
Explanation:
Hope this helps dude
Answer:
Pascal's Law = C
Archimedes's Law = B
Bernoulli's Law = A
Explanation:
Alrighty, here are the prinicples needed:
In Pascal's law, he states that the pressure applied to an enclosed fluid is directly transmitted without the change in magnitidue. With that, magnitude in every point of the fluid and the walls of the container are remained unchanged. To say simply,the fluid is equal to the pressure at any point in all directions.
\(P=\frac{F}{A}\)
Where:
F = Force
A = Area
Archimedes Law states that the buoyant force is the weight of the fluid displaced. When any boat displaces a weight of water equal to its own weight, it floats. This is often called the “principle of flotation” where a floating object displaces a weight of fluid equal to its own weight.
\(F_{b} = -pgV\)
Fb = buoyant force
-p = fluid density
g = acceleration due to gravity
V = fluid volume
The Bernoulli law states that total energy per unit mass of flowing fluid, at any point in the subsurface, is the sum of the kinetic, potential, and fluid-pressure energies and is equal to a constant value.
I hope that this provided you with some clarification and that you have a nice day. I would be happy to help you again in the future. :D
Develop and maintain operational and process documentation for the HPC environment. Ensure the HPC environment continues to provide the necessary diverse set of services to support complex campus research requirements.
In conclusion, developing and maintaining operational and process documentation for the HPC environment involves identifying services, documenting procedures and workflows, providing examples, and regularly updating the documentation. This ensures that the HPC environment continues to support complex campus research requirements effectively.
To develop and maintain operational and process documentation for the HPC (High Performance Computing) environment, there are several steps you can follow:
1. Identify the diverse set of services required: Understand the specific research requirements of the campus and determine the different services that the HPC environment needs to support.
2. Document operational procedures: Create step-by-step instructions for tasks such as system setup, software installation, user access management, and data backup. These documents should provide clear guidelines for administrators to follow.
3. Document process workflows: Define the processes involved in running specific research tasks on the HPC environment. This could include data preprocessing, job submission, monitoring, and result analysis. Documenting these workflows helps ensure consistency and reproducibility.
4. Provide examples and illustrations: Include examples and diagrams to make the documentation more understandable. For instance, you could include screenshots of the user interface, sample scripts, or flowcharts to illustrate the workflows.
5. Update and review regularly: As the HPC environment evolves, ensure that the documentation remains up-to-date. Regularly review and revise the content to reflect any changes in hardware, software, or research requirements.
In conclusion, developing and maintaining operational and process documentation for the HPC environment involves identifying services, documenting procedures and workflows, providing examples, and regularly updating the documentation. This ensures that the HPC environment continues to support complex campus research requirements effectively.
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a current of 12 A flows through a fan for 30 minutes.How many charge flows through then fan during this time?
Answer:
Q=21600C
Explanation:
Q=It.
Data
I=12A
t=30min
convert time from minutes to second
t=60*30
=1800s
Q=?
Q=It
=(12A)*(1800s)
Q=21600C
28. Ratman's rat mobile is traveling at 80m/s North when it turns on its rocket boosters
accelerating the rat mobile to 200 m/s in 4 seconds.
What's the rat mobiles acceleration?
The acceleration of rate mobile is 30 m/s².
Given - Initial velocity=80m/s , Final Velocity=200m/s , time= 4sec
To find out acceleration.
Principle- Acceleration means rate of change of velocity. Mathematically derivative of velocity with the function of time is acceleration.
a=dv/dt
a=(vₙ-v )/dt
substitute vₙ=200m/s , v=80m/s , dt=4sec
a= [ 200 -80 ]/4
a= 120/4
acceleration ⇒ a=30 m/s²
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This photo shows a cactus plant. Its thick, fleshy stems have a waxy coating. How do the stems help the cactus plant survive?
A. They take minerals from the soil.
B. They shade the plant from sunlight.
C. They hold the plant in the ground.
D. They hold water in the plant
The stems help the cactus plant survive by ;D. They hold water in the plant.
How the cactus survivesThe thick, fleshy stems of a cactus plant have the ability to store water. This is an important adaptation that allows the plant to survive in arid environments with limited water availability.
The waxy coating on the stems helps to prevent water loss through evaporation. The stored water in the stems can be utilized by the cactus during periods of drought or when water is scarce, enabling the plant to survive for extended periods without rainfall.
Therefore, option D is the most accurate choice as it describes how the stems of a cactus plant help it survive by storing water.
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what is the speed of a wave a wavelength of 2.3 meters and a frequency of 5 Hz
Explanation:
The speed of a wave can be calculated using wavelength, Frequency.speed = wavelength x frequency.The wavelength of the wave is 2.3 meters.The frequency of the wave is 5 Hz.So,
speed = wavelength x frequency
speed = 2.3 meters x 5 Hz => 11.5 meters per second
Therefore, the speed of the wave is 11.5 meters per second.
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what is
contact force
Answer:
Contact forces are forces that act between two objects that are physically touching each other.
An object has a mass of 20 kg and a volume of 5 mL. What is the object's density?
the answer is 4 kg/cm 3. but how do I get to this conclusion?
Think of a cube that is 1 cm by 1 cm by 1 cm. The volume of this cube is 1*1*1 = 1 cubic cm = cm^3. This is equivalent to 1 mL by definition
So the object's volume of 5 mL is the same as 5 cm^3.
To get the density of an object, we divide the mass over volume
density = (mass)/(volume)
density = (20 kg)/(5 mL)
density = (20 kg)/(5 cm^3)
density = (20/5) (kg/cm^3)
density = 4 kg/cm^3
The density is 4 kilograms per cubic centimeter. In other words, each cubic centimeter of volume has about 4 kilograms of material.
You can tell from reading this passage that -
the narrator will definitely find a diamond at the Crater of Diamonds State Park.
diamonds are rare, valuable gems.
garnet is as valuable as a diamond.
semi-precious stones are ugly.
Answer: B or "diamonds are rare,valuable gems".
Explanation:
since the link does not show very much, I don't know if A is correct or not. D is incorrect because that is an opinion. C is incorrect.
which one of the following is true of an object moving in a circle at constant speed? a the object has an acceleration along a tangent to the circular motion.. b all statements above are false. c the direction of the velocity of the object is changing. d the object has a velocity towards the center of the circle.
Option c is correct. The direction of velocity of an object changes. During uniform circular motion, speed is constant, but the direction changes at every point. So, velocity changes due to a change in direction.
When an object is moving on a circular path with constant speed, motion is called uniform circular motion. During such motion, speed is constant, but velocity changes due to changes in direction at every point on the curve. The direction of velocity is along the tangent at every point.
There is acceleration which has a direction towards the center. This acceleration causes centripetal force. Due to this force object moving in a circular path continuously changes direction and is capable of moving in a circular path.
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Jeremy hypothesized that adults with blue eyes are shorter than adults with brown eyes. He collected data by visiting all of the teachers in his school and found that his hypothesis was false. Should Jeremy consider his hypothesis useful?
A.
Yes; now he knows that the exact opposite of his hypothesis must be true.
B.
Yes; a false hypothesis gives a scientist new information to use.
C.
No; a false hypothesis makes a scientist look silly.
D.
No; false hypotheses are a waste of time.
Answer: B. Yes; a false hypothesis gives a scientist new information to use.
Explanation:
Let us take a look and break down all the question's answer options.
✗ A.
Yes; now he knows that the exact opposite of his hypothesis must be true.
➜ This is not the case. He must look at this data and decide what is true.
✓B.
Yes; a false hypothesis gives a scientist new information to use.
➜ Yes! We learn from our research and looking back at our hypothesis.
✗ C.
No; a false hypothesis makes a scientist look silly.
➜ This isn't true. You cannot expect to be right all the time, and scientists make incorrect hypotheses frequently.
✗ D.
No; false hypotheses are a waste of time.
➜ Tying back into B and C, this isn't true. We learn from comparing our hypotheses with our data.
The Washington Monument is 169 meters tall.
A worker assigned to the restoration of the Washington Monument is checking the condition of the stone at the very top of the monument. A nickel with a mass of 0.005 kg is in her shirt pocket.
Q: If the nickel accidentally falls out of her pocket, what will happen to the gravitational potential energy (GPE) of the nickel as it falls to the ground?
The gravitational potential energy (GPE) of the nickel will increase as it falls to the ground due to the force of gravity acting on it.
When an object falls, it gains kinetic energy, which is the energy of motion. As an object falls, it gains kinetic energy at the expense of its potential energy.
The amount of GPE gained will be equal to the mass of the nickel multiplied by the acceleration due to gravity and the change in height from the worker's pocket to the ground. Specifically, the change in GPE = 0.005 kg \(* 9.8 m/s^2 * 169\)* m. As the nickel falls it will accelerate and its kinetic energy will increase as well. The nickel will convert the potential energy into kinetic energy and also will gain velocity as it falls, reaching a terminal velocity.
When the nickel reaches the ground, all of its potential energy will have been converted into kinetic energy.
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Val warms up some soup on the stove. Assuming no phase change has occurred, what effect does warming have on the soup?
Its particles have less kinetic energy.
Its particles have more kinetic energy.
Its specific heat increases.
Its specific heat decreases.
Val warms up some soup on the stove and there is no phase change, then the effect of warming the soup is that its particles will have more kinetic energy. Hence, option B is correct.
What is Kinetic energy?Kinetic energy is the type of energy that an item or particle possesses as a result of its motion. When work, that transfers energy, is performed on an item by exerting a resultant force, the object accelerates and obtains kinetic energy.
Kinetic energy is a feature of an object moving or particle affected from both its speed and is affected by both its speed and its mass. Rotation, rotation about a plane, vibrations, or any combinations of motions are all possible.
When val warms the soup, the bond between the molecule further break and the space between them will also increase due to which they do random movement and their velocity will also increase and when velocity then by the formula the kinetic energy will also increase.
Therefore, the particles have more kinetic energy.
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Two in-phase sources of waves are separated by a distance of 3.99 m. These sources produce identical waves that have a wavelength of s.s them, there are two places at which the same type of interference occurs. (a) Is it constructive or destructive int interference? (b) and (c) Where are these places located occurs. (the smaller distance should be the answer to (b)) (a (b) Number 2.96 (c) NumberT Units
(a)The interference between the two waves produced by the in-phase sources is constructive (c) the locations where the same type of interference occurs are at angles of 44.6° and 79.1° with the line joining the two sources. (b )The smaller distance is 2.96s.s .
The given problem involves two in-phase sources of waves that are separated by a distance of 3.99 m. These sources produce identical waves with a wavelength of s.s them, and we need to find out the locations where the same type of interference occurs and whether it is constructive or destructive interference.
(a) To determine whether the interference is constructive or destructive, we need to calculate the phase difference between the two waves. If the phase difference is an even multiple of π (i.e., 0, 2π, 4π, etc.), the interference is constructive. If the phase difference is an odd multiple of π (i.e., π, 3π, 5π, etc.), the interference is destructive. In this case, the phase difference between the two waves is zero since they are in-phase. Therefore, the interference is constructive.
(b) To find the locations where constructive interference occurs, we need to use the formula d sinθ = mλ, where d is the distance between the two sources, θ is the angle between the line joining the two sources and the line perpendicular to the screen, m is an integer, and λ is the wavelength of the waves. For constructive interference, m can be 0, ±1, ±2, etc. The smallest distance at which the same type of interference occurs corresponds to m = 1. Thus, we have 3.99 sinθ = 1s.s them, which gives sinθ = 1s.s them/3.99. Solving for θ, we get θ = sin⁻¹(1s.s them/3.99) ≈ 44.6°. Therefore, the location where constructive interference occurs is at an angle of 44.6° with the line joining the two sources.
(c) To find the other location where constructive interference occurs, we need to use the same formula as above but with m = 2. Thus, we have 3.99 sinθ = 2s.s them, which gives sinθ = 2s.s them/3.99. Solving for θ, we get θ = sin⁻¹(2s.s them/3.99) ≈ 79.1°. Therefore, the other location where constructive interference occurs is at an angle of 79.1° with the line joining the two sources.
In conclusion, the interference between the two waves produced by the in-phase sources is constructive, and the locations where the same type of interference occurs are at angles of 44.6° and 79.1° with the line joining the two sources. The smaller distance between these two locations is 2.96s.s them, and the units of the answer depend on the units used for the wavelength.
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