Problem 22.51 A slab of insulating material has thickness 2d and is oriented so that its faces are parallel to the yz- plane and given by the planes crd and = -d. The y- and 2-dimensions of the slab are very large compared to d, so treat them as infinite. The slab has charge density given by p(x) = po (c/d)', where po is a positive constant. Part A Using Gauss's law, find the magnitude of the electric field due to the slab at the center of the slab 2 = 0). Express your answer in terms of some or all of the variables po, d, 3 and electric constant Eo. IV ALQ R O O ? Ex=0 = Submit Request Answer Part B Identify direction of the electric field due to the slab in different areas. Drag the labels to their appropriate locations in the diagram. Labels can be used once, more than once, or not at all. O va 0 d

Wavenumber (and frequency) drop from left to right, and peaks in an IR spectrum grow downward.

An absorption technique that is frequently used in both qualitative and quantitative investigations is infrared (IR) spectroscopy. The electromagnetic radiation in the infrared area of the spectrum has the ability to change the rotational and vibrational states of covalent bonds in organic molecules.

In addition to a variety of other uses, infrared spectroscopy (IR) is used to determine chemical species, identify chemical species, quantify chemical species, and determine molecular structure. Utilizing this method, scientists may examine matter in its solid, liquid, and gaseous phases.

An atom or group of atoms inside a molecule that exhibits a comparable set of chemical characteristics across a variety of compounds is referred to as a functional group.

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The plane of a loop of wire is perpendicular to a magnetic field. Rank from greatest to least, the magnitudes of the loop's induced emf for each situation will be E - B - D - A - C.

The number of magnetic flux lines on a unit area passing perpendicular to the given line direction is known as induced magnetic field strength. It is denoted by B.

The magnitude of the induced EMF in the loop of wire is:

∈ = ΔФ/ Δt

The magnetic flux is given by ФB = ΔBA

∈ = ΔBA / Δt

The above expression shows that the induced emf is proportional to the rate of change of the magnetic field.

ΔB/Δt = (1T-0T)/6 = 0.167 T/sec

ΔB/Δt = (4T-1T)/2 = 1.500 T/sec

ΔB/Δt = (4T-4T)/60 = 0 T/sec

ΔB/Δt = (3T-4T)/4 = -0.25 T/sec

ΔB/Δt = (0T-3T)/1 = -3 T/sec

From the above, it is observed that rank, from the greatest to least, the magnitudes of the loop's induced emf for each situation will be

E - B - D - A - C.

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YES, Many consumers have concerns about changing their incandescent bulbs because they are unsure of how LED light bulbs operate. Using dimmable LED light bulbs in sockets without a dimmer switch is one often requested query.

Compared to conventional incandescent bulbs, LED light bulbs have many benefits. The key benefits are longer life, less heat, and less electricity usage. Non-dimmable LED lights are becoming less and less available from shops. As a result, it is almost certain that you will need to use a conventional socket to install a dimmable LED light.

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Answer:

Below

Explanation:

Her POTENTIAL energy , mgh , is converted to KINETIC energy , 1/2 mv^2

mgh = 1/2 mv^2     You can divide through by 'm' to get:

gh = 1/2 v^2       solve for 'v'

v = sqrt (2gh)

   = sqrt ( 2 * 9.81 * 25.8) = 22.5 m/s

( NOTE that her mass, 64.6 kg , is irrelevant)

You a generally safe inside an automobile during a lighting storm because the metal car body will carry the lightning current around the passengers inside.

Storm, violent atmospheric disturbance, characterised by low barometric pressure, cloud cowl, precipitation, sturdy winds, and probable lightning and thunder.

Current the flow of electrical charge vendors, typically electrons or electron-deficient atoms. The not unusual image for present day is the uppercase letter I. the same old unit is the ampere, symbolized with the aid of A

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Doppler shift or Doppler impact is described because the alternate in frequency of sound wave because of a reflector shifting in the direction of or farfar from an object.

This is which withinside the case of ultrasound is the transducerλ is one wave period, then the quantity of wave lengths N which are found in a two-manner communique direction among the Radar and goal might be same to 2R/λ.

We realize that one wave period λ corresponds to an angular tour of 2π radians.The Doppler shift may be decided after appearing the variety Fourier transform (variety FFT) first. For a goal of interest, we are able to repeat the variety FFT till we've sufficient information to carry out the second one degree of FFT.

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The mass flow rate of the liquid is found to be 152,135 Lbs/hr.

The volume flow rate is given to be 332 gpm.

It means that 332 gallons per minute is flowing.

The density of the liquid is given to be 58 lbs/ft³.

We have to calculate the mass flow rate in lbs/hr.

The amount of liquid flowing in one hour is = 332×60 gallons per hour.

= 19920 gallons per hour.

1 gallon = 0.134 ft³

Converting,

The amount of liquid flowing in one hour is,

= 19920×0.134 ft³/h

= 2609.52 ft³/h.

Now,

Density = Mass/volume

Putting values,

58.30 = Mass/2609.52

Mass flow rate = 152,135.016 lbs/h.

Rounding off to the nearest Whole number.

So, the mass flow rate of the liquid is 152135 lbs/h.

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Answer:

Therefore, the approximate value of y for x = 4 is approximately 0.97.

Explanation:

To determine the approximate value of y for x = 4, we need to use the values in the table to find a mathematical relationship between x and y. This can be done by performing a linear regression analysis on the data.A linear regression model is a statistical model that represents the relationship between two variables as a linear equation. The equation of the line is given by:y = mx + bWhere m is the slope of the line and b is the y-intercept (the point where the line crosses the y-axis).We can use the values in the table to calculate the values of m and b. Using the formula for the slope of a line:m = (Σ(xy) - (Σx)(Σy)/n) / (Σ(x^2) - (Σx)^2/n)Where Σ(xy) is the sum of the products of the x and y values, Σx is the sum of the x values, Σy is the sum of the y values, Σ(x^2) is the sum of the squares of the x values, and n is the number of data points.Plugging in the values from the table, we get:m = (1146.07 - (69.7)(625.99)/5) / (1152.64 - (69.7)^2/5)m = 0.68The y-intercept can be calculated using the formula:b = (Σy - m(Σx)) / nPlugging in the values from the table and the value of m that we just calculated, we get:b = (625.99 - 0.68(69.7)) / 5b = -1.75We can now use the values of m and b to write the equation of the line:y = 0.68x - 1.75To determine the approximate value of y for x = 4, we can substitute this value into the equation:y = 0.68 * 4 - 1.75y = 2.72 - 1.75y = 0.97

The focal length of the mirror formed by the convex side of a shiny spoon will be 0.0205 m.

As per the question,

It is given that,

The radius of curvature R=2.41 cm

We know, for determining the relationship between focal length and radius of curvature we have the following relationship:

[tex]\mathrm{f}=\frac{\mathrm{R}}{2}[/tex]

So, for determining the value of focal length we will put the value of the radius of curvature in the above formula.

Thus, we will get,

[tex]\mathrm{f}=\frac{2.41}{2}\\\mathrm{f}=1.205 \mathrm{~cm}\\\mathrm{f}=0.0205 \mathrm{~m}\\f=-0.0205 m[/tex]

As the focal length of the mirror is formed by the convex side of the shiny spoon. So, for denoting it we used a negative sign.

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The total resistance will ne 80. The amount that a resistor adds to the circuit's overall resistance depends on how it is connected.

When connecting electrical components, there are two options. Parallel circuits connect components along parallel branches, whereas series circuits connect components one after the other.

Ohm's Law, which states that voltage equals current times resistance, if you don't know the specific values of each resistance.

In a series circuit, the current is constant throughout the whole circuit.  The supply voltage is the same as the total voltage (the battery). It differs from the voltage across a single component.

Therefore, The total resistance will ne 80. The amount that a resistor adds to the circuit's overall resistance depends on how it is connected.

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Ranking in order, from largest to smallest, their wave speeds : [tex]v_{a}=v_{b}=v_{c}[/tex]

What is Wave speed?

The amount of space a wave covers in a certain length of time, such as the number of metres it covers in a second, is known as its wave speed. Speed = Wavelength x Frequency is an equation that describes how wave speed relates to wave wavelength and wave frequency.

Wave pulses in stretched string, wave speeds, and medium are notions that must be understood in order to answer the provided issue.

Find the factors that impact the medium's wave speed first. Next, evaluate the three waves and order them by speed.

Given by, is the wave speed,

ν=nλ

Here, v is the wave speed, n is the frequency, and λ is wavelength.

The same stretched string is being followed by all three waves. Therefore, the medium is the same for all three strings.

Only the wave medium has the ability to alter a wave's speed.

The wave speed for the same medium is unaffected by the frequency and wavelength of any of the three waves. The criterion to evaluate the waves would be frequency and wavelength if the medium were different for each of the three waves.

Due of their shared medium of motion, all three waves will move at the same pace. thus only the characteristics of the medium have an impact on wave speed.

[tex]v_{a}=v_{b}=v_{c}[/tex]

The three waves use the same medium. The wave velocity will thus be the same. The wave speed will vary depending on the medium, and it may be rated.

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The center of mass is 2.25 which is point C.

A place at which the entire mass of a body or all the masses of a system of particles appears to be concentrated is defined as the center of mass of a body or system of particles.

The center of mass for straightforward stiff objects with homogeneous density is found at the centroid. The center of mass will always rest immediately underneath a shape if it is suspended from a single point. Therefore, the center of mass is where two lines that are drawn down downward from two different places on a shape (one at a time) intersect.

Here, we have 5 masses so the center of mass will be at the third block.

But here we remove a block and the left masses are:

o.5, 1.5, 2.5 and 4.5

X(cm) = m(0.5) + m(1.5) + m(2.5) + m(4.5) / 4m

X(cm) = m(0.5 + 1.5 + 2.5 + 4.5) / (4) m

[m will be cancelled out]

X(cm) = 9 / 4 = 2.25 which is point C

Therefore, the center of mass is 2.25 which is point C.

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Answer: In cases a, b, and c, the only force acting on the stone is the force of gravity, mg, straight downward. In case d, the force of gravity also acts straight downward, however, there is an applied force with greater magnitude acting upward.

Note that this explanation assumes that drag (air resistance) is negligible.

The force acting on the 2 m wire carrying a 2 A current and placed in a 4 T magnetic field is 16 N.

The subject of this question is Physics, particularly dealing with the concept of magnetic force. In this scenario, we are asked to determine the magnitude of the force acting on a wire that is carrying a current and placed within a magnetic field. The force on a current carrying conductor in a magnetic field can be calculated using the formula F=BIL, where F is the magnetic force, B is the magnetic field strength, I is the current in the wire, and L is the length of the wire.

In this problem, we are given B=4 T, I=2 A, and L=2 m. Substituting these values into the equation, we find that F=BIL=(4 T)*(2 A)*(2 m)=16 N.

Therefore, the correct answer is D. 16 N.

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hydrogen, accounts for 74% of the mass while helium contributes 25%. Heavier elements comprise less than 1% of the total.This universe was 13.7 billion years old, adding or subtracting approximately 130,000 years, as determined by NASA's WMAP probe.

The vast quantities of helium and hydrogen that were created during the Big Bang account for the majority of the chemical elements' abundance in the cosmos.Only 2% of the universe's mass is made up of remaining elements, which were primarily created by supernovae and some red giant stars.

As the only element in the cosmos without a neutron, hydrogen is the most basic in the universe, that explains why it is also the most plentiful, according to Nyman. Hydrogen has just one proton one and electron.

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The internal resistance of the battery is 0.1988 ohms and the emf of the battery is 8015 v

Given

V1=8.2 V

I1 =1.54 A

and

V2=9.2 V

I2=-3.49 A (since it is in reverse direction)

a)

since

E= V1+I1r

E=V2+I2r

V1+I1r =V2+I2r

8.2+1.54r =9.2-3.49r

5.03r =1

Resistance r=0.1988 ohms

b)

E=V1+I1r =8.2+1.54*0.1988

E=8.51 V

The effort required to transfer a unit of positive electric charge from one location to another is known as potential difference.  

Due to the potential difference between the two ends of the battery, if you connect the two ends of the same wire to the opposite ends of the same battery, electricity will flow through it.

Work is done by the component when electrons travel through it. The component receives a portion of the electrons' energy

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If a wooden plank 2 m long, 30 cm wide, and 40 mm thick floats in water with 10 mm of its thickness above the surface, the mass of the board is 18 kg.

Calculation:-

mass of board = density of water x volume of water displaced

= 1000 x 2x0.3x0.03

= 18 kg.

A property of a body that is a measure of inertia is usually viewed as a measure of the amount of matter contained in the body that causes it to have weight in a gravitational field. Mass is a dimensionless quantity that describes the amount of matter in a particle or object.

The mass of an object is a measure of its inertial properties or the amount of matter it contains. The weight of an object is a measure of the force exerted on it by gravity, or the force required to support it. Mass can best be understood as the amount of matter present in an object or body. Everything around us has mass.

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Image result for Find the phase difference between these two rays at point B, ignoring any phase shift due to reflection.

Two sound waves of the same frequency that are perfectly aligned have a phase difference of 0 and are said to be “in phase.” Two waves that are in phase add to produce a sound wave with an amplitude equal to the sum of the amplitudes of the two waves. This process is called “constructive interference.

Phase difference ​​= 2πλx path difference.

When the phase difference between the waves is an even multiple of (180°), constructive interference happens, but destructive interference happens when the difference is an odd multiple of.

The location of neighboring medium particles vibrating in phase is known as the wavefront. Because of this, there is no phase difference between any two places on a wavefront.

By operating in the X-Y mode, the CRO can measure the phase difference. The pattern that CRO predicts is a diagonal straight line making 45° with the X-axis at a phase shift of = 0° or 360°. The pattern that CRO predicts at a phase shift of = 90° is a clockwise spinning circle.

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When the quantity of energy entering and leaving the Earth's atmosphere is not the same, radioactive forcing results.

A radioactive forcing is an energy imbalance that the climate system is subjected to, either externally or as a result of human activity ( changes in solar energy output, volcanic anthropogenic emissions of greenhouse gases, aerosols, and their precursors; intentional land change.

In other words, if you want to know how to tell if something is good or bad, you need to know how to tell if it's good or bad.

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The final linear velocity of the solid wood cylinder just before it hits the ground is 8.85 m/s.

The final linear velocity of the hollow metal cylinder just before it hits the ground is 7.7 m/s.

The final linear velocities of the two cylinders just before they hit the ground is calculated by applying the principle of conservation of energy.

translational kinetic energy + rotational kinetic energy = gravitational potential energy

¹/₂mv²  + ¹/₂Iω² = mgh

where;

The moment of inertia of solid cylinder, I = ¹/₂mr²

¹/₂mv²  + ¹/₂Iω² = mgh

¹/₂mv²  + ¹/₂(¹/₂mr²)(v/r)² = mgh

¹/₂mv²  + ¹/₄(mr²)(v²/r²) = mgh

¹/₂mv²  + ¹/₄(mv²) = mgh

¹/₂v²  + ¹/₄v² = gh

2v² + v² = 4gh

3v² = 4gh

v² = 4gh/3

v = √ (4gh / 3)

v = √ (4 x 9.8 x 6 / 3)

v = 8.85 m/s

The moment of inertia of hollow cylinder, I = mr²

¹/₂mv²  + ¹/₂Iω² = mgh

¹/₂mv²  + ¹/₂(mr²)(v/r)² = mgh

¹/₂mv²  + ¹/₂(mr²)(v²/r²) = mgh

¹/₂mv²  + ¹/₂(mv²) = mgh

¹/₂v²  + ¹/₂v² = gh

2v²  = 2gh

v² = 2gh / 2

v² = gh

v = √ (gh)

v = √ (9.8 x 6)

v = 7.7 m/s

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When a solar-mass star will evolve off the main sequence when it loses all its neutrinos, so fusion must cease it builds up a core of inert helium.

The right order of evolutionary levels for a solar mass big name is: principal sequence, horizontal department, asymptotic branch, white dwarf. The electricity that fuels the sun is generated: best in its core.

Sooner or later, a chief series megastar burns through the hydrogen in its core, attaining the quit of its existence cycle. At this factor, it leaves the main sequence.

Stars smaller than 1 / 4 the mass of the solar collapse directly into white dwarfs. White dwarfs now not burn fusion at their center, however they still radiate warmness.

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A)  The constant of proportionality, K is 840 B) The current when the resistance is 12 ohms is 70 amperes.

The resistance R and the current I are inversely related.

I=k/R   (k is the constant of proportionality)

A) I=210 amperes

    R=4 ohms

    I=k/R

    k=I×R

    k=210×4=840

B)   R=12 ohms

      k=840

      I=k/R

      I=840/12=70 amperes

Another significant characteristic in electrical systems that can be measured is resistance. Ohms. are the units. used to measure. resistance. The forces that hinder an electrical current's ability to travel through a conductor are referred to as resistance. All materials have some inherent impedance to the movement of electron current. We haven't figured out how to create conductors without any resistance.

Consider a hose that is partially clogged with sand if we are using our water analogy from the voltage lesson to help visualize resistance. The water in the hose will flow more slowly due to the sand. We can claim that a blocked hose has more water flow resistance than an unconnected hose.

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Increase in the volume of water produced by thermal expansion creates a corresponding rise in sea level

What is thermal expansion?

Solids, liquids, and gases all exhibit the phenomena known as thermal expansion. This process involves the expansion of an object or body when heat is applied (temperature). Thermal expansion is the tendency of an object to change its dimensions as a result of heat, including length, density, area, or volume. The substance has more kinetic energy when it is heated.

Three forms of thermal expansion exist:

According to the question:

Sea level rise is brought on by a larger volume of ocean water as a result of thermal expansion. The amount of water in the oceans is also rising as a result of melting ice and snow on land brought on by rising temperatures. Sea level will only rise as a result of land-based ice and snow melting.

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The particle follows the path indicated in the figure, hitting the bottom plate. The mass of the particle and the magnitude of the charge on each plate factors determine the time the particle takes to reach the bottom plate.

What occurs when an electrically charged particle moves?

Magnetic force fields are produced by charged particles in motion. Charged particles that are accelerated create shifting electric and magnetic force fields that travel as EM waves. Polarized electromagnetic radiation (EMR) has all electric and magnetic field variations along the same plane.

A charged particle moves because of what?

Charged particles may move in spiral or elliptical patterns as a result of magnetic fields. Protons are kept on circular courses by particle accelerators using magnetic force. When cosmic rays come into contact with an astronomical object or planet's magnetic field, they will travel in spiral patterns.

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The particle follows the path indicated in the figure, hitting the bottom plate. The mass of the particle and the magnitude of the charge on each plate factors determine the time the particle takes to reach the bottom plate.

Magnetic force fields are produced by charged particles in motion. Charged particles that are accelerated create shifting electric and magnetic force fields that travel as EM waves. Polarized electromagnetic radiation (EMR) has all electric and magnetic field variations along the same plane.

Charged particles may move in spiral or elliptical patterns as a result of magnetic fields. Protons are kept on circular courses by particle accelerators using magnetic force. When cosmic rays come into contact with an astronomical object or planet's magnetic field, they will travel in spiral patterns.

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The frequency of the variation is 324.04 KHz.

Frequency is the wide variety of occurrences of a repeating event in step with unit time. For clarity, additionally called temporal frequency, which isn't like angular frequency. Frequency is measured in hertz (Hz) and corresponds to one occasion in keeping with 2nd. duration is the reciprocal of frequency, because duration is the time c program languageperiod between activities.

Frequency is an critical parameter utilized in technology and engineering to explain the speed of vibrations and vibrational phenomena inclusive of mechanical vibrations, audio indicators (sound), radio waves, and mild.

calculation :

[tex](\frac{lambda}{4} ) + (\frac{lambda}{4}) = 5.74 mm[/tex]

[tex]lambda = 11.48 m = 11.48*10^{-3} m[/tex]

Now,

[tex]f = \frac{v}{lambda} = \frac{3.72*10^{3} }{11.48*10^{-3} }[/tex]

                 [tex]= 324041.81 Hz[/tex]

                 [tex]= 324.04 KHz[/tex]

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An object is thrown with a horizontal velocity of 20 m/s from a vertical cliff that is 125 m above level ground. If air resistance is negligible, the time that it takes the object to fall to the ground from the cliff is nearly Five (5) seconds.

The horizontal velocity is the speed at which an object is traveling in a straight line. It can vary from object to object and can be affected by a number of factors. One of these factors is air resistance. Air resistance is a force that acts in the opposite direction to the motion of an object. It is a result of the air molecules pushing back against the object as it moves through it. The amount of air resistance acting on an object depends on its shape and size, as well as the speed at which it moves.

This means that as an object's horizontal velocity increases, the amount of air resistance acting on it also increases. This can slow down the object's velocity, or even cause it to come to a stop.

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The induced electromotive force is larger in magnitude if the magnetic field is turned off more quickly when the vector points into the page.

We know that, as per faraday's law,

= Induced EMF = d(Ф)dt

where Ф  is magnetic flux

Thus, Ф = BA

so,

Induced EMF = d(BA) / dt

We can see time in inversely related to emf. So if we switch off the magnetic field in less time then EMF will be more.

Therefore, answer should be "The induced electromotive force is larger in magnitude if the magnetic field is turned off more quickly."

Next, the current should follow Lenz's law and t should oppose the change in magnetic flux.

The induced current should flow clockwise.

Now, we know

Induced emf = d(BA)/ dt

where A = pi X r²

So, if radius is doubled then,

= A = π X (2r)²

= A = 4 X pi X r²

Hence,

Emf increases by 4 times ( it quadruples ).

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DataT2 vs L in a straight-line fit of the data have been plotted in an experiment .

Pendulum: a body that is hung from a fixed location and moves back and forth as a result of gravity. Pendulums are employed to control clock movement because the period—the amount of time between each full oscillation—is constant.

A pendulum is a straightforward illustration of energy transfer since it repeatedly transforms potential energy into kinetic energy until it comes to a halt due to the minimal amount of power lost to heat or air resistance.

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2.0 m/s is the maximum speed. 200 m/s2 is the maximum acceleration. Calculating the angular frequency is necessary. utilising the angular frequency formula.

Fill out the formula with the value A stretched string is traversed by a sinusoidal wave. A particle on the string can move at a maximum speed of 0.900 m/s and accelerate at a maximum rate of 270 m/s2. What are the wave's frequency and amplitude?

On stretched string, a sinusoidal wave travelling in the right direction has an amplitude of 20 cm, a wavelength of 1, and a speed of 5 m/s. It is assumed that y=0 and dtdy0 at x=0 and t=0. the wave function for y. (x,t).

A particle on the string can move at a maximum speed of 0.900 m/s and accelerate at a maximum rate of 270 m/s2. What are the wave's frequency and amplitude?

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