Would you expect the smallest guitar string to produce waves in the glass of water at a higher or lower frequency?

To resolve the star-planet system at a distance of 4 light-years, a telescope on Earth would need an aperture with a minimum diameter of 55.88 mm.

In optical microscopy, the Rayleigh criterion is frequently used to estimate the resolution of the microscope. The resolution limit imposed by this criterion has long been regarded as a roadblock to using an optical microscope to study biological phenomena at the nanoscale.

We can use the Rayleigh criterion,

θ = 1.22 λ / D

θ = angular resolution

λ = wavelength of light

D = diameter of the telescope's aperture

θ = arctan (r / d)

r = radius of the planet's orbit

d = distance to the star

Now, we use the given values,

r = 149.6×106 km = 149.6×109 m

d = 4 × 9.461×1015 m = 3.7844×1016 m

λ = 550 nm = 550×10-9 m

θ = arctan (r / d)

   =arctan (149.6×109 / 3.7844×1016) = 0.000012 radians

we can use the Rayleigh criterion,

θ = 1.22 λ / D

D = 1.22 λ / θ

D = 1.22 × 550×10-9 / 0.000012

D = 55.88 mm

To know more about the Rayleigh criterion visit:

https://brainly.com/question/19953205

#SPJ1

The electric force between two point charges is given by the equation

[tex]F=k*q_1*q_2/r^2[/tex]

The interaction between two things is measured by the physical quantity known as force. It is a vector quantity, and the sign F is frequently used to denote it. When an object interacts with another object, it feels a push or a pull.

where r is the distance between the charges, q1 and q2 are their magnitudes, and k is the Coulomb constant.

When we enter the problem's specified values, we obtain

[tex]2.2N=8.99*10^9\ N*m^2/C^2*q*-2q/(1.4 m)^2[/tex]

which simplifies to

q = -0.500 N/C.

Thus, the magnitude of charge q is 0.500 N/C.

To learn more about force, visit:

brainly.com/question/12785175

#SPJ1

The original temperature of the mercury is 260.6K

To solve this problem, we can use the formula for the heat released during the solidification of a substance:

Q = m * Lf

where Q is the heat released, m is the mass of the substance, and Lf is the heat of fusion of the substance.

In this case, Q = 157 kJ, m = 5.00 kg, and Lf = 11.3 kJ/kg.

We also need to use the formula for the heat absorbed or released during a temperature change:

Q = m * c * ΔT

where Q is the heat absorbed or released, m is the mass of the substance, c is the specific heat of the substance, and ΔT is the change in temperature.

We can use this formula to calculate the heat released as the mercury cools from its original temperature to its melting point, and then use the formula for solidification to calculate the heat released as the mercury solidifies.

Let T be the original temperature of the mercury.

The heat released as the mercury cools from its original temperature to its melting point is:

Q1 = m * c * (T - 234)

The heat released as the mercury solidifies is:

Q2 = m * Lf

The total heat released is:

Q = Q1 + Q2 = m * c * (T - 234) + m * Lf

Substituting the values given in the problem, we get:

157 kJ = 5.00 kg * 140 J/kg . K * (T - 234) + 5.00 kg * 11.3 kJ/kg

Simplifying and solving for T, we get:

T = 260.6 K

Therefore, the original temperature of the mercury was 260.6 K.

Learn more about Energy here:

https://brainly.com/question/13881533

#SPJ1

The system's final temperature is roughly 16.7°C.

You may determine your substance's final heat by multiplying the temperature change by the initial temperature. Your water's final temperature would be 24 + 6, or 30 degrees Celsius, for instance, if it started off at 24 degrees Celsius.

The following is the formula for energy conservation:

Q1 + Q2 = 0

Q = mcΔT

Q1 + Q2 = 0

568.8

Simplifying and solving for

6394.4 - 106768 = 0

= 16.7°C

To know more about temperature visit:-

https://brainly.com/question/4160783

#SPJ1

Answer:

B. Atomic number minus mass number

Explanation:

Two or greater sources are said to be coherent if they emit waves that have the identical wavelength (or frequency) and amplitude and which maintain a steady phase difference.

If two sources have the identical wavelength, frequency, and segment difference, they are said to be coherent. Therefore, we can conclude that coherent sources have the identical wavelength.

Two microwave coherent factor sources emitting waves of wavelenths λare positioned at 5λdistance apart. The interference is being observed on a flat non-reflecting surface alongside a line passing through on sources ,in a course perpendicular to the line joining the two sources

Learn more about coherent waves here:

Humans would need a breathable environment like that on Earth in the living section of a colony on Venus in order to survive. Nitrogen, oxygen, and trace amounts of other gases, such as carbon dioxide, make up the majority of the atmosphere on Earth.

The clouds are made of sulfuric acid, and the atmosphere is primarily carbon dioxide, the same gas that causes the greenhouse effect on Venus and Earth. And the heated, high-pressure carbon dioxide acts corrosively at the surface.

For instance, compared to Earth, which has 99% nitrogen and oxygen in its atmosphere, Venus and Mars both contain more than 98% carbon dioxide and nitrogen.

To know more about atmosphere visit:-

https://brainly.com/question/885615

#SPJ1

The wavelength of the electron is 1.724 × 10^-12 m.

The wavelength of the electron is found  using the de Broglie wavelength formula:

λ = h / p

where λ = wavelength,

h= Planck's constant, a

p =  momentum of the electron.

we find  the momentum of the electron,

p = m * v

p = (9.1 × 10^-31 kg) * (4.2 × 10^7 m/s)

p = 3.822 × 10^-22 kg m/s

Therefore, wavelength ;

λ = h / p

λ = (6.6 × 10^-34 J s) / (3.822 × 10^-22 kg m/s)

λ = 1.724 × 10^-12 m

Learn more about wavelength at: https://brainly.com/question/10728818

#SPJ1

Answer:

ttrockstars

Explanation:

it's math you to be an expert at math thank you

A cesium-133 atom's radiation goes through 1.5 million cycles in around 0.1633 microseconds (or 163.3 nanoseconds).

9,192,631,770 hertz (cycles per second) is the frequency of the microwave spectral line that the isotope cesium-133 emits. The basic unit of time is provided by this. Cesium clocks have an accuracy and stability of 1 second in 1.4 million years.

The radiation emitted by cesium-133 has a frequency of 9,192,631,770 cycles per second, or 9.192631770 109 Hz.

The following formula may be used to determine how long 1.5 million radiation cycles take to complete:

Time is equal to the frequency of cycles.

Plugging in the numbers, we get:

time = 1.5 million / 9.192631770 × 10^9 Hz

time = 1.632995101 × 10^-7 seconds

So it takes approximately 0.1633 microseconds (or 163.3 nanoseconds) for radiation from a cesium-133 atom to complete 1.5 million cycles.

To know more about cesium-133 visit:-

https://brainly.com/question/4830355

#SPJ1

a) The time after the release of the first stone that the second stone hits the water is 2.0 s.

b) 15.7 m/s is the initial speed of the second stone.

c)  The speed of the first stone as it hits the water is 15.7 m/s.

d) The speed of the second stone as it hits the water is 28.2 m/s.

Velocity is a vector quantity that measures both the speed and direction of an object's motion. It is equal to the rate of change of an object's position with respect to time. Velocity is usually represented by the symbol v and is measured in meters per second (m/s).

a) The time between first and second stone's release is 1.0 s. Since the time of release of first stone and the time of splash of both stones are same, the time between the release of second stone and the splash of both stones is 1.0 s.

Thus, the time after the release of the first stone that the second stone hits the water is 2.0 s.

b) The initial speed of the second stone can be calculated using the equation of motion,

v² = u² + 2as

where v is the final velocity, u is the initial velocity, a is the acceleration due to gravity (9.8 m/s²), and s is the displacement.

Substituting the values,

v² = (1.7)² + 2(9.8) * 59

v = 15.7 m/s

c) The speed of the first stone as it hits the water can be calculated using the equation of motion,

v² = u² + 2as

where v is the final velocity, u is the initial velocity, a is the acceleration due to gravity (9.8 m/s²), and s is the displacement.

Substituting the values,

v² = (1.7)² + 2(9.8) * 59

v = 15.7 m/s

d) The speed of the second stone as it hits the water can be calculated using the equation of motion,

v² = u² + 2as

where v is the final velocity, u is the initial velocity, a is the acceleration due to gravity (9.8 m/s²), and s is the displacement.

Substituting the values,

v² = (15.7)² + 2(9.8) * 59

v = 28.2 m/s

For more questions related to initial speed

https://brainly.com/question/24493758

#SPJ1

The speed of the waves can be expressed to two significant figures as 0.2 m/s. The unit for this expression is meters per second (m/s).

A wave crest is the highest point of a wave. It is the top of the wave, where the wave is moving most up and away from the equilibrium position. It is the point of highest amplitude (height) of the wave and is followed by a wave trough, which is the lowest point of the wave.

The speed of the waves can be calculated using the formula speed = distance over time.

We know the distance between wave crests is 9.0 m and the time it takes for 12 waves to pass the boat is 45 s. Therefore, the speed of the waves can be calculated as:

Speed = 9.0 m / 45 s

Speed = 0.2 m/s

The speed of the waves can be expressed to two significant figures as 0.2 m/s. The unit for this expression is meters per second (m/s).

This calculation shows that the speed of the waves passing the boat is 0.2 m/s. This speed can be further broken down into how many meters the waves travel in one second if necessary.

For more questions related to speed

https://brainly.com/question/13943409

#SPJ1

The Universe became dominated by matter instead of radiation at a redshift of around 3300.

To determine at what redshift the Universe became dominated by matter, we need to find the redshift at which the energy density of matter becomes equal to the energy density of radiation.

Let's start with the energy density of radiation, which can be calculated using the Stefan-Boltzmann law:

$[tex]u_{rad} = \frac{4\sigma}{c}T^4$[/tex]

where $\sigma$ is the Stefan-Boltzmann constant, $c$ is the speed of light, and $T$ is the temperature of the radiation. Since we are assuming that the cosmic microwave radiation is a black-body radiation, we can use the temperature of 2.73 K, which corresponds to the peak of the radiation curve:

[tex]$u_{rad} = \frac{4\sigma}{c}(2.73K)^4 \approx 0.261 \text{ eV/cm}^3$[/tex]

Next, let's calculate the energy density of matter. We know that the number density of baryons is [tex]$n_b \approx \frac{1}{10^9}n_{\gamma}$, where $n_{\gamma}$[/tex] is the number density of photons. Since we are assuming that the photon-to-baryon ratio is constant, we can write:

[tex]$\frac{\rho_b}{\rho_{\gamma}} = \frac{m_b n_b}{\frac{4}{3}\sigma T^4} = \frac{3m_b}{4\sigma T^3 n_{\gamma}} \approx \frac{3m_b}{4\sigma T^3}\frac{1}{n_{\gamma}}$[/tex]

where $m_b$ is the mass of a baryon. Substituting the values, we get:

[tex]$\frac{\rho_b}{\rho_{\gamma}} \approx 4.15 \times 10^{-10}$[/tex]

Since the total energy density of the Universe is given by:

[tex]$\rho_{tot} = \rho_b + \rho_{\gamma}$[/tex]

we can write:

[tex]$\frac{\rho_b}{\rho_{tot}} = \frac{\rho_b}{\rho_b + \rho_{\gamma}} \approx \frac{\rho_b}{\rho_{\gamma}} = 4.15 \times 10^{-10}$[/tex]

At the redshift $z$, the energy density of radiation will be diluted by a factor of $[tex](1+z)^4[/tex]$, while the energy density of matter will be diluted by a factor of $[tex](1+z)^3[/tex]$. Thus, at some redshift $z$, we will have:

$  [tex]\frac{\rho_b}{\rho_{tot}} = \frac{\rho_b}{\rho_b + \rho_{\gamma}} = \frac{1}{1+z}\frac{3m_b}{4\sigma T^3 n_{\gamma}}[/tex]   $

Setting this equal to the value we calculated above, we can solve for $z$:

$   [tex]\frac{1}{1+z}\frac{3m_b}{4\sigma T^3 n_{\gamma}} \approx 4.15 \times 10^{-10}[/tex]  $

$  [tex]1+z \approx \frac{3m_b}{4\sigma T^3 n_{\gamma}}\frac{1}{4.15 \times 10^{-10}}[/tex]  $

$ [tex]z \approx 3300[/tex] $

Therefore, the Universe became dominated by matter instead of radiation at a redshift of around 3300.

To know more about density:

https://brainly.com/question/29775886

#SPJ1

The above has to do with the study of the earth's lithospheric plates. See the attached image and the explanation below.

The movement of lithospheric plates is a geological process that occurs due to the motion of hot, molten material in the Earth's mantle. The lithosphere, which is the rigid outer layer of the Earth's surface, is divided into several large plates that move relative to each other.

These movements are caused by the convection of material in the mantle and the forces that arise at the boundaries between the plates.

There are three main types of plate boundaries: divergent, convergent, and transform. Divergent boundaries occur where plates move apart from each other, creating new oceanic crust. Convergent boundaries arise where plates collide, leading to subduction, volcanic activity, and the formation of mountains. Transform boundaries occur where plates slide past each other.

The movement of lithospheric plates gives rise to various geological phenomena, such as earthquakes, volcanic activity, and the formation of mountain ranges and ocean basins.

Learn more about movement of lithospheric plates:
https://brainly.com/question/2722711
#SPJ1

Answer:

A) P.E = 138.44 J

B) The velocity of swing at bottom, v = 3.33 m/s

C) The work done, W = -138.44 J

Explanation:

Given,

The mass of the child, m = 25 Kg

The length of the swing rope, L = 2.2 m

The angle of the swing to the vertical position, ∅ = 42°

A) The potential energy at the initial position ∅ = 42° is given by the relation

                               P.E = mgh joule

Considering h  = 0 for the vertical position

The h at ∅ = 42° is  h = L (1 - cos∅)

                              P.E = mgL (1 - cos∅)

Substituting the given values in the above equation

                              P.E = 25 x 9.8 x 2.2 (1 - cos42°)

                                     = 138.44 J

The potential energy for the child just as she is released, compared to the potential energy at the bottom of the swing is, P.E = 138.44 J

B) The velocity of the swing at the bottom.

At bottom of the swing the P.E is completely transformed into the K.E

                 ∴                 K.E = P.E

                                    1/2 mv² = 138.44

                                    1/2 x 25 x v² 138.44

                                           v² = 11.0752

                                            v = 3.33 m/s

The velocity of the swing at the bottom is, v = 3.33 m/s

C) The work done by the tension in the rope from initial position to the bottom

            Tension on string, T = Force acting on the swing, F

                           =

                           = - 2.2 x 25 x 9.8 [cos0 - cos 42°]

                           = - 138.44 J

The negative sign in the in energy is that the work done is towards the gravitational force of attraction.

The work done by the tension in the ropes as the child swings from the initial position to the bottom of the swing, W = - 138.44 J

A sound that is 7.8x10-4 W/m2 in intensity is equal to (10 dB)log3.2106 W/m21012 W/m2=185 dB.

The decibel, often known as the db or 0.1 bel, is the standard measurement unit. Hence, b = 10 log10 (I/I0) can be used to express the relationship between relative intensities, or b, in decibels. This equation can be used to determine that one decibel equals a 26 percent intensity variations.

The "decibel level" of a sound is a less formal term for relative intensity level. It is not the same as energy; relative intensity level reflects loudness more faithfully by using a logarithmic scale.

To know more about sound visit :

https://brainly.com/question/29707602

#SPJ1

A heat engine with a 65.0% Carnot efficiency is currently being developed. Between a reservoir that is 25.00C and one that is 3750C, a heat engine is operational.

The equation is: Carnot efficiency is equal to 1 - Tc/Th, wherein Tc is the cycle's cold end temperature and Th is its hot end temperature. In other words, efficiency is equal to one minus the difference between the hot and cold temperatures.

Explanation: The cold reservoir's temperature is TL=20C=20+273=293K. T L = 20 ∘ C = 20 + 273 = 293 K .

A Carnot cycle running between both of these two reservoirs has a thermal efficiency of = 1 TC/TH. This value exceeds the value of the Otto cycle, which is operating between similar reservoirs by a large margin.

Two know more about efficiency visit:

https://brainly.com/question/13021831

#SPJ1

Answer: d. increase

Explanation:

If the sun were more massive, the gravitational force between the sun and Earth would increase. This means that Earth's gravity with the sun would also increase. Therefore, the correct answer is (D) increase.

The gravitational force between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. So, if the mass of one of the objects increases, the gravitational force between them will also increase. In this case, if the mass of the sun were to increase, the gravitational force between the sun and Earth would become stronger, and hence, Earth's gravity with the sun would also increase.

The light ray will deviate from its original path with 19.5° after refraction.

Applying Snell's law to calculate the angle of refraction:

n1 sin θ1 = n2 sin θ2

where n1 and θ1 =  the refractive index and the angle of incidence in the first medium (air),

n2 and θ2 =  the refractive index and the angle of refraction in the second medium (glass).

In this example,

n1 = 1.00 (refractive index of air), θ1 = 30°, and

n2 = 1.5 (refractive index of glass).

We then calculate for  θ2:

n1 sin θ1 = n2 sin θ2

1.00 * sin 30° = 1.5 * sin θ2

0.5 = 1.5 * sin θ2

sin θ2 = 0.5 / 1.5 = 1/3

θ2 = sin^-1(1/3)

θ2 = 19.5°

Learn more about Snell's law at:

https://brainly.com/question/2273464

#SPJ1

Answer:A

Explanation:

Isotopes are members of a family of an element that all have the same number of protons but different numbers of neutrons. The number of protons in a nucleus determines the element's atomic number on the Periodic Table.

Answer:

Explanation:

Because you have velocity along the y axis and time along the x axis, this is a velocity v time graph which is an acceleration graph. The slope of the line in this graph IS the acceleration. We can use 2 points and the slope formula to solve for the acceleration:

(0, 0) and (1, 3):

[tex]m=\frac{3-0}{1-0}=3[/tex] m/s squared, choice D.

The value of the charge on each particle is [tex]1.05 x 10^-8 C[/tex].

Coulomb's law is a fundamental principle of electrostatics that describes the interaction between electric charges. It states that the force between two point charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. We can use Coulomb's law to solve this problem. Mathematically,

[tex]F = k(q1q2)/r^2[/tex]

where F is the force of attraction or repulsion between the two charged particles,[tex]q1[/tex] and [tex]q2[/tex] are the magnitudes of the charges on the two particles, r is the distance between them, and k is Coulomb's constant, which has a value of [tex]9.0 x 10^9 Nm^2/C^2.[/tex]

In this problem, we know that the charges are equal and the distance between them is 10.0 cm. We also know that the force between them is 0.5 N. Therefore,

[tex]0.5 N = k(q^2)/(0.1 m)^2[/tex]

Solving for q, we get:

[tex]q = \sqrt{[(0.5 N)(0.1 m)^2/k]}[/tex]

[tex]q = \sqrt{(0.5 N)(0.01 m)/(9.0 x 10^9 Nm^2/C^2)}[/tex]

[tex]q = 1.05 x 10^-8 C[/tex]

Therefore, the value of the charge on each particle is [tex]1.05 x 10^-8 C.[/tex]

Learn more about electrostatics here:

https://brainly.com/question/31042490

#SPJ1

The final temperature after adding the ice to the water and calorimeter will be approximately 8.37 ◦C.

What is Temperature?

Temperature is a measure of the average kinetic energy of the particles in a substance or system. It is a scalar quantity that indicates how hot or cold an object or medium is. Temperature is commonly measured using various scales, such as Celsius (°C), Fahrenheit (°F), and Kelvin (K), which represent different reference points and units of measurement.

Since energy is conserved, we can set Q_ice equal to Q_water+calorimeter:

m_ice * c_ice * ΔT_ice = (m_water + m_calorimeter) * c_water+calorimeter * ΔT_water+calorimeter

27 g * 2090 J/kg ◦C * (T_f + 65) = (525 g + 80 g) * (4186 J/kg ◦C + 387 J/kg ◦C) * (T_f - 25)

Simplifying and solving for T_f:

27 * 2090 * (T_f + 65) = 605 * (T_f - 25)

56130 T_f + 361350 = 605 T_f - 15125

56130 T_f - 605 T_f = -15125 - 361350

-44,970 T_f = -376475

T_f = (-376475) / (-44,970)

T_f ≈ 8.37 ◦C

Learn more about Temperature from the given link

https://brainly.com/question/26866637

#SPJ1

Answer:

correlation is defined as the statistical association between two variables

Explanation:

a correction exits between two variables when one of them is related to the other in some way