Wednesday

September 17, 2014

September 17, 2014

Total # Posts: 246

**Acoustic**

Consider a room that is 6m long, 5m wide and 3m high and whose walls, floor and ceiling have the same sound absorption coefficient (α=0.01). When all machines are in use, the sound pressure level (SPL) within the room amounts to 90 dB. A carpet is to be placed on the ...
*September 11, 2014*

**Acoustic**

How would you expect the directivity of the piston to vary as the temperature of air decreases? (Hint: Low temperature -> decrease of sound speed) 1.Directivity of the piston is independent of the temperature. 2.Directivity of the piston becomes smooth (low directivity) ...
*September 11, 2014*

**Acoustic**

A breathing sphere of radius 0.1m radiates spherical waves into air at 100Hz with an intensity of 200mW/m2 at the distance 0.5m from the center of the sphere. In this case, 1) Compute the radiated acoustic power. 2) Compute the intensity at the surface of the sphere. 3) ...
*September 11, 2014*

**Music**

List one of the vocal technology topics and describe how it has changed and/or affected popular music. 1. Time Based Effects Processing 2. Autotune or Melodyne 3. Talkbox or Vocoder 4. Vocal Sampling 5. Elastic Audio and Flex
*July 14, 2014*

**Astronomy**

The current peak wavelength of the CMB corresponds to a blackbody of temperature 2.74K. What was the peak wavelength of the CMB when it was emitted? The current redshift of the CMB is z=1100. Give your answer in microns. Which waveband regime is this?
*June 24, 2014*

**Astronomy**

What about a for a supernova in an elliptical galaxy of 10^12 solar masses and radius of 50 kpc? Yes or No
*June 24, 2014*

**Astronomy**

Supernovae can eject material at velocities of 0.001c. Will gas ejected by a supernova which occurs inside a dwarf galaxy with a mass of 10^8 Msolar and a radius of a few kpc be able to escape the galaxy? Yes or No
*June 24, 2014*

**Astronomy**

The star Polaris has a surface temperature of roughly 6500 K and a radius of approximately 50 solar radii. Find the luminosity of Polaris in terms of the Sun's luminosity.
*June 24, 2014*

**Astronomy**

A galaxy is receding away from us with a recession velocity of 100,000 km/s. What is the distance to this galaxy? What is the redshift z of this galaxy?
*June 24, 2014*

**Astronomy**

A quasar is observed at a redshift of z=1, which corresponds to a comoving radial distance of 3 Gpc. Its observed bolometric flux is 10^{-12} erg/cm^2/s. An interacting companion galaxy is seen 4 arcsec apart in projection. What is the bolometric luminosity of the quasar, in ...
*June 19, 2014*

**Maths Probability**

3) 0.0625
*May 20, 2014*

**Probability**

A dedicated professor has been holding infinitely long office hours. Undergraduate students arrive according to a Poisson process at a rate of per hour, while graduate students arrive according to a second, independent Poisson process at a rate of per hour. An arriving ...
*May 13, 2014*

**Probability**

Uncle Henry has been having trouble keeping his weight constant. In fact, during each week, his weight changes from the beginning of the week to the end of the week by a random amount, uniformly distributed between -0.5 and 0.5 pounds. Assuming that his weight change during ...
*May 13, 2014*

**Probability**

Suppose that you move to a new house and you are 10% sure that your new house's phone number is 561290. To verify this, you use the house's phone to dial 561290, obtain a busy signal, and conclude that this is indeed your phone number. (Suppose that you were incorrect...
*May 13, 2014*

**Astronomy**

Imagine that you have found an object out in space. When you use the inverse square law to compute its luminosity, you get a ridiculously large value. You therefore suspect that relativistic beaming is at work - the radiation is coming from a jet traveling at speed v directly...
*May 11, 2014*

**Astronomy**

Imagine that you are an astronomer, and you are planning to do a survey to find new brown-dwarf stars. You need to calculate how sensitive your search needs to be (and hence how big a telescope you will need and how long the survey will take). You want to find ten times more ...
*May 11, 2014*

**Astronomy**

Imagine that you are a particle physicist, and you have come up with a theory that some gamma-ray bursts come from the decay of a new and exotic sub-atomic particle that you think might exist. You calculated that if this particle really does exist and decay as you predict, ...
*May 11, 2014*

**Astronomy**

The luminosity of the Sun is 4*10^33 erg/s, and its radius is 7*10^10 cm. What is the Sun's effective temperature? Please enter your answer in units of Kelvin.
*May 6, 2014*

**Astronomy**

black hole of mass 2 * 10 ^ 30 kg
*May 4, 2014*

**Astronomy**

Imagine you are in a spaceship one million km from a black hole of mass kg. Initially you are flying directly away from it at a velocity of 16.9 km/s. Using the n-body approximation, what is your velocity one second later? Type your answer in metres per second.
*May 4, 2014*

**Astronomy**

The luminosity of the Sun is 4*10^33 erg/s, and its radius is 7*10^10 cm. What is the Sun's effective temperature? Please enter your answer in units of Kelvin. What is the Sun's effective temperature? Please enter your answer in units of Kelvin. - unanswered What is ...
*April 29, 2014*

**Astronomy**

Choose one answer for each question How old is the universe? 6,000 years old 380,000 years old 13.8 billion years old 13.8 million years old A parsec is: Longer than a light year The distance between the Earth and the Sun Approximately 3x10^24 cm None of the above The distance...
*April 29, 2014*

**Probability**

We are given the following statistics about the number of children in the families of a small village. There are 100 families: 10 families have no children, 40 families have 1 child each, 30 families have 2 children each, 10 families have 3 each, and 10 families have 4 each. ...
*April 29, 2014*

**Probability**

All ships travel at the same speed through a wide canal. Each ship takes days to traverse the length of the canal. Eastbound ships (i.e., ships traveling east) arrive as a Poisson process with an arrival rate of ships per day. Westbound ships (i.e., ships traveling west) ...
*April 29, 2014*

**Probability**

In parts 1, 3, 4, and 5 below, your answers will be algebraic expressions. Enter 'lambda' for and 'mu' for . Follow standard notation. 1. Shuttles bound for Boston depart from New York every hour on the hour (e.g., at exactly one o'clock, two o'clock, ...
*April 29, 2014*

**Probability**

Fred is giving away samples of dog food. He makes visits door to door, but he gives a sample away (one can of dog food) only on those visits for which the door is answered and a dog is in residence. On any visit, the probability of the door being answered is 3/4 , and the ...
*April 29, 2014*

**Astronomy**

Another possible energy source would be gravity. Imagine that the strange object contains a black hole of mass mbh. You drop a star of mass m into it. If the star of mass m starts at rest at infinity, what will the kinetic energy of the star be when it crosses the event ...
*April 28, 2014*

**Astronomy**

One possible energy source for the mysterious object you've just discovered is the fusion of hydrogen to form carbon-12 (the most common and stable isotope of Carbon). Hydrogen has an atomic mass of 1.00794 u, while carbon has an atomic mass of 12.010 u. If you fuse ...
*April 28, 2014*

**Astronomy**

Imagine that a rival astronomer proposes that your mysterious object is actually the mouth of a wormhole to another dimension. The rival astronomer calculates that the wormhole mouth would need to be 10^13 m in diameter and would last for around a thousand years. Which one or ...
*April 28, 2014*

**Astronomy**

Imagine that you have just discovered a strange object. This object is a distance D away, has a redshift z, and you measure a flux for it f. Derive an equation for the luminosity L of this object.
*April 28, 2014*

**Probability**

For any given flight, an airline tries to sell as many tickets as possible. Suppose that on average, 10% of ticket holders fail to show up, all independent of one another. Knowing this, an airline will sell more tickets than there are seats available (i.e., overbook the flight...
*April 27, 2014*

**Astronomy**

A roughly spherical asteroid with a diameter of 1 km, and a mean density of 4 g/cm^3, hits the Earth with a relative speed 1.5 times the orbital velocity of the Earth. Compute the amount of energy released upon the impact. Compare that with the energy released by a 10-Megaton ...
*April 25, 2014*

**Probability**

Let X be a continuous random variable. We know that it takes values between 0 and 3 , but we do not know its distribution or its mean and variance. We are interested in estimating the mean of X, which we denote by h . We will use as a conservative value (upper bound) for the ...
*April 21, 2014*

**Probability**

The random variables X1,..,Xn are independent Poisson random variables with a common parameter Lambda . Find the maximum likelihood estimate of Lambda based on observed values x1,...,xn.
*April 21, 2014*

**Probability**

For any given flight, an airline tries to sell as many tickets as possible. Suppose that on average, 10% of ticket holders fail to show up, all independent of one another. Knowing this, an airline will sell more tickets than there are seats available (i.e., overbook the flight...
*April 21, 2014*

**Probability**

Let Sn be the number of successes in n independent Bernoulli trials, where the probability of success for each trial is 1/2 . Provide a numerical value, to a precision of 3 decimal places, for each of the following limits. 1. lim P (n/2 - 20 < Sn < n/2 + 20) 2. lim P (n/...
*April 21, 2014*

**Astronomy**

In the past few million years of Mars the main source of climate variation has been the slow escape of the atmosphere. Probably true Maybe Probably false
*April 21, 2014*

**Astronomy**

Sometimes a crater from the Noachian period can be found inside of a crater from the Amazonian period. Probably true Maybe Probably false.
*April 21, 2014*

**Astronomy**

The northern plains of Mars have many characteristics that you would expect from their being an ancient ocean floor. Probably true Maybe Probably false
*April 21, 2014*

**Astronomy**

Rain was once common on Mars. Probably true Maybe/unclear Probably false
*April 21, 2014*

**Astronomy**

Rank the following hypothetical planets -- all of which have the same total mass and same radius -- from lowest moment of inertia to highest moment of inertia: 1) A uniform sphere of mixed up rock and iron 2) A hollow sphere 3) A rocky planet with an iron core 4) A rocky ...
*April 21, 2014*

**Astronomy**

Which of the following statements is correct? (check all that apply) If liquid water is not stable on the surface of Mars, liquid CO2 is definitely not stable. If liquid CO2 is not stable on the surface of Mars, liquid water is definitely not stable. If liquid water is stable ...
*April 21, 2014*

**Probability**

a=? b=?
*April 20, 2014*

**Probability**

θˆLMS= ?
*April 20, 2014*

**Probability**

Random variables X and Y are distributed according to the joint PDF fX,Y(x,y) = {ax,0,if 1≤x≤2 and 0≤y≤x,otherwise.} 1. Find the constant a. 2. Determine the marginal PDF fY(y). (Your answer can be either numerical or algebraic functions of y). For 0&#...
*March 18, 2014*

**Probability**

Let X and Y be normal random variables with means 0 and 2, respectively, and variances 1 and 9, respectively. Find the following, using the standard normal table. Express your answers to an accuracy of 4 decimal places. 1. P(X>0.75)= 2. P(X≤−1.25)= 3. Let Z=(Y&#...
*March 18, 2014*

**Probability**

Consider the following joint PMF of the random variables X and Y: pX,Y(x,y)={1/72⋅(x2+y2),if x∈{1,2,4} and y∈{1,3}, 0, otherwise}. 1. P(Y<X)= 2. P(Y=X)= 3. Find the marginal PMF pX(x). pX(1)= pX(2)= pX(3)= pX(4)= 4. Find E[X] and E[XY]. E[X]= E[XY]= 5. var...
*March 7, 2014*

**Probability**

We start with a collection of n (distinguishable) individuals whom we want to split into three possible teams: the blue team, the red team, and the white team. Each individual is randomly assigned to exactly one of the teams according to the following procedure. An individual ...
*March 7, 2014*

**Probability**

To get a complete collection of stamps, Ann needs to have 5 specific (and different) kinds of stamps, denoted by k1,…,k5. She starts out with no stamps. She then receives 5 stamps randomly from a lottery. Each of these 5 stamps has probability 1/5 of being of any ...
*March 7, 2014*

**Probability**

Alice has five coins in a bag: two coins are normal (i.e., fair with one face Heads and the other face Tails), two are double-headed (i.e., both sides are Heads), and the last one is double-tailed (i.e., both sides are Tails). She reaches into the bag and randomly pulls out a ...
*March 7, 2014*

**Probability**

For each of the following statements, determine whether it is true (meaning, always true) or false (meaning, not always true). Here, we assume all random variables are discrete, and that all expectations are well-defined and finite. Let X and Y be two binomial random variables...
*March 4, 2014*

**Astronomy**

What is the estimated total lifetime for a star with mass 0.7 Msun ? (in billions of year)
*March 4, 2014*

**Astronomy**

The coolest star whose peak blackbody wavelength can be observed with the human eye (the exact range of visible light varies from publication to publication, so use 380nm to 750 nm).
*March 4, 2014*

**Astronomy**

How close to the sun Ganymede would have to be in order to hold water in its atmosphere. (in AU)
*March 4, 2014*

**Astronomy**

A newly discovered planet has a surface temperature of 330 K and a density of 6 g/cm3. What minimum radius does the planet need to have in order to hold water in its atmosphere indefinitely? (in km)
*March 4, 2014*

**Astronomy**

Imagine you are on some far away planetary system looking for planets in the galactic neighborhood and you spot our sun in your sky. In degrees, what is the maximum the orbit can be tilted from 90 in order to see a transiting eclipse (assume the longitude angle is 0)?
*March 4, 2014*

**Probability**

Consider 10 independent tosses of a biased coin with the probability of Heads at each toss equal to p , where 0 < p < 1 . 1. Let A be the event that there are 6 Heads in the first 8 tosses. Let B be the event that the 9th toss results in Heads. Find P(B|A) and express it...
*February 28, 2014*

**Probability**

You are given the set of letters ( A, B, C, D, E ). What is the probability that in a random five-letter string (in which each letter appears exactly once, and with all such strings equally likely) the letters A and B are next to each other?
*February 23, 2014*

**Probability**

The newest invention is a three-sided die. On any roll of this die, the result is 1 with probability 1/2, 2 with probability 1/4, and 3 with probability 1/4. Consider a sequence of six independent rolls of this die. 1. Find the probability that exactly two of the rolls results...
*February 23, 2014*

**Probability**

A group of 90 students is to be split at random into 3 classes of equal size. All partitions are equally likely. Joe and Jane are members of the 90-student group. Find the probability that Joe and Jane end up in the same class.
*February 23, 2014*

**Probability**

A player is randomly dealt a sequence of 13 cards from a standard 52-card deck. All sequences of 13 cards are equally likely. In an equivalent model, the cards are chosen and dealt one at a time. When choosing a card, the dealer is equally likely to pick any of the cards that...
*February 23, 2014*

**Probability**

Alice plays the following game with Bob. First, Alice randomly chooses a set of 4 cards out of a 52-card deck, memorizes them, and places them back into the deck. (Any set of 4 cards is equally likely.) Then, Bob randomly chooses 8 cards out of the same deck. (Any set of 8 ...
*February 23, 2014*

**Chemistry**

The following questions concern the iconic Nestle Toll House Chocolate Chip Cookie recipe, shown below: 2 1/4 cups all-purpose flour 1 teaspoon baking soda 1 teaspoon salt 1 cup butter or margarine, softened 3/4 cup granulated sugar 3/4 cup packed brown sugar 1 teaspoon ...
*October 10, 2013*

**Chemistry**

The following questions concern the iconic Nestle Toll House Chocolate Chip Cookie recipe, shown below: 2 1/4 cups all-purpose flour 1 teaspoon baking soda 1 teaspoon salt 1 cup butter or margarine, softened 3/4 cup granulated sugar 3/4 cup packed brown sugar 1 teaspoon ...
*October 10, 2013*

**Chemistry**

1)Buttermilk has 9 grams of protein and 12 grams of carbohydrate per cup (237ml). Estimate the concentration in mol/L of protein using the fact that the average protein is 300 amino acids long and the average amino acid has a mass of 110 amu. 2)Lactose (MW:342 amu) makes up ...
*October 10, 2013*

**Chemistry**

Identify the major macronutrient by weight in each of the following key ingredients. Olive oil Carbohydrates Fats Proteins Buttermilk/milk Carbohydrates Fats Proteins Neither Distilled vinegar Carbohydrates Fats Proteins Plain Greek yogurt Carbohydrates Fats Proteins Which ...
*October 10, 2013*

**Chemistry**

Which nutrient is most abundant (by weight) in eggplants? Carbohydrates Fats Proteins Add up the total mass of carbohydrates, fats, and proteins in a serving of eggplant. What fraction of the eggplant's weight is made up of these ingredients? Which of the following ...
*October 10, 2013*

**Astronomy**

Basically the ``Bohr radius'' for the dark matter is rB=ℏ^2 / GN M m^2 where m is the dark matter mass, M is the total amount of dark matter mass contained inside the ``gravitational atom'', and ℏ and GN are constants as usual. Taking the dark ...
*October 1, 2013*

**Astronomy**

How the asymmetry between matter and anti-matter in our Universe might be generated. Why might neutrinos be a key player in achieving this? (a) We already know neutrinos can morph from one neutrino type to another. It is possible, although not certain, that neutrinos could ...
*October 1, 2013*

**Astronomy**

What percentage of the energy budget do electrons occupy? Take the energy budget occupied by matter to be 4.4%. (a) 3.9% (b) 0.1% (c) 0.03% (d) 0.002%
*October 1, 2013*

**Astronomy**

The Universe is filled with a frozen in Higgs condensate. If this were to suddenly disappear/evaporate, what would happen? (a) All bound matter—nucleons (made of quarks), nuclei (made of nucleons), atoms (made of nuclei and electrons), people (made of atoms), etc.—...
*October 1, 2013*

**Astronomy**

What were the relative energy densities in the early Universe? (below, DE means dark energy) (a) They remain roughly equal: rad ∼ mat ∼ DE (b) DE > mat > rad (c) rad > mat > DE (d) mat > rad >...
*October 1, 2013*

**Astronomy**

Which of the below statements about the CMB are true? (i) The “hot” and “cold” spots are areas where photons have slightly more or less energy than average. (ii) It shows that the Universe was accelerating at the time the CMB formed, thus measuring dark ...
*October 1, 2013*

**Astronomy**

Now imagine you’re an astronomer on Earth looking at the spectrum of an object in space. In the spectrum you are looking for the so-called Lyman-alpha line of hydrogen which occurs at a wavelength of = 122 nm. In your telescope, you observe the Lyman-...
*October 1, 2013*

**Astronomy**

How do we image dark matter? (a) We see light from galaxies behind the bullet cluster that is bent (gravitationally lensed) due to the matter (regular and dark) in the bullet cluster. (b) We see light from the gas in the two bullet cluster galaxies and we observe that the gas ...
*October 1, 2013*

**Astronomy**

Where did CMB radiation originate? (a) It is the radiation from the electroweak phase transition when the weak force was spon- taneously broken by the Higgs mechanism. (b) It is radiation from supernovas in the early Universe that produced the heavier elements. (c) The ...
*October 1, 2013*

**Astronomy**

Why didn’t the Universe collapse into a black hole in the past when there was so much matter in such a small space? (a) Most of the particles in the early Universe were unstable and decayed before a black hole could form. By the time only stable particles were left (...
*October 1, 2013*

**Astronomy**

Each time period corresponds with an event in the list below labeled a to e. Starting with the earliest time period (10^−34 s), list which time period corresponds to which event. For example if you think the times at 10^−34 s, 10^−12 s, 10^−10 s, 3 min...
*October 1, 2013*

**Astronomy**

Look up where Voyager 1 is now and compute how many lighthours it is away. Round your answer to the nearest number of light hours.
*September 17, 2013*

**Astronomy**

What is the size, i.e. the radius, of a black hole with a mass equal to that of Earth (MEarth=6×1024kg)? Give your answer to one significant figure.
*September 17, 2013*

**chemistry**

A particle with the mass of a proton is trapped in a box. The particle falls from the n=3 state to the n=2 state and emits 0.16 meV of energy. What is the size of the box? Please report your answer in nm.
*September 16, 2013*

**Quantum Physics**

What is the maximum value of the wavelength of light that will ionize the hydrogen atom? Express your answer in units of nanometers.
*April 22, 2013*

**Quantum Physics**

Consider the observable M that corresponds to a measurement in the sign basis where the measurement value is 3 if the outcome is + and -2 if the outcome is - A)Write M in the standard basis. B)If M is the Hamiltonian acting on a qubit which is in the state |phy(0)> = |0>...
*April 16, 2013*

**Quantum Physics**

thanks Andy,Flu and everyone worked for this subject!
*April 16, 2013*

**Quantum Physics**

All wrong?
*April 16, 2013*

**Quantum Physics**

5A: (2/K), (1 - 2/K) 5B: (-2/K), (2/K - 1) 5C: (2/K - 1), (-2/K)
*April 16, 2013*

**Quantum Physics**

Suppose we ran m steps of Grover's algorithm on some function f (which has one marked element y) and the resulting superposition was exactly |y⟩. If we run for m+1 additional steps (i.e. total of 2m+1 steps from the initial state), what is the resulting ...
*April 16, 2013*

**Quantum Physics**

Consider a particle whose wavefunction at some fixed time t is represented by -A if -2≤x≤0 ψ(x)= A if 0≤x≤3 0 otherwise (a) What is the normalization constant A? (b) What is the probability of finding the particle at a position x≤0? (c) What ...
*April 6, 2013*

**Quantum Physics**

Suppose a particle has wavefunction ψ(x,t=0)=Ae^(−x^2/l^2). What is the average value (expectation value) of p, <p>, for this state at t=0?
*April 3, 2013*

**Quantum Physics**

Suppose we have a particle in 1-dimension, with wavefunction Ae^(−|x|/2d). What is the probability to find the particle in the interval [0,d]?
*April 3, 2013*

**Quantum Physics**

The ground state wavefunction for a particle in a shallow potential well in 1 dimension is of the form: Ae^(−|x|/2d). Given that the particle must be found somewhere in the range x∈[−∞,∞], the born rule then places a constraint on the modulus of A...
*April 3, 2013*

**Biochemistry**

Nicotine is a small molecule produced by the tobacco plant Nicotiana tabacum. Nicotine is produced by the plant to discourage herbivores. In low doses, such as those experienced by tobacco users, it is a stimulant that leads to mild euphoria. In high doses, it acts as a potent...
*March 31, 2013*

**Biochemistry**

Amylase is secreted by your pancreas into your small intestine where amylase helps you digest the starches in your diet. Amylase does this because it is an enzyme, a protein that catalyzes a chemical reaction. In this case, amylase catalyzes the breakdown, or hydrolysis, of ...
*March 30, 2013*

**Genetics**

β-thalassemia is a human genetic disease that is inherited in an autosomal recessive manner. Individuals with β-thalassemia produce abnormal hemoglobin which results in a reduced ability to carry oxygen in their blood. The severity of symptoms depends on several ...
*March 27, 2013*

**Quantum Physics**

Let f:{0,1}->{0,1} with f(101)=1 and f(x)=0 for x ≠ 101 . In this question, we will run through two iterations of the algorithm. (a) What is the superposition after the initialization step? Note that you can describe the superposition Σαx|x> by ...
*March 25, 2013*

**Quantum Physics**

Help please!
*March 24, 2013*

**Genetics**

Consider the following cross involving the genes for pod color and seed shape: P generation: Green pods with round seeds= ____ Yellow pods with wrinkled seeds=____ F1 generation: 1/4 green pods with round seeds= ____ 1/4 grens pods with wrinkled seeds=____ 1/4 yellow pods with...
*March 21, 2013*

**Genetics**

Remember that the upper-case letter corresponds to the allele with the dominant phenotype. Use the symbols "A" and "a" for pod color and the letters "B" and "b" for seed shape.
*March 21, 2013*

**Genetics**

Mendel also studied pod color, which could be green or yellow, as well as seed shape, which could be round or wrinkled. Consider the following cross: P generation: Yellow pods with round seeds=____ Green pods with wrinkled seeds=____ F1 generation 100% Green pods with round ...
*March 21, 2013*

**Genetics**

Mendel also studied the trait of flower color. Some plants had white flowers, while others had purple flowers. Consider the following cross: P generation: Plant with purple flowers= ____ Plant With purple flowers= ____ F1 generation: 75% plant with purple flowers= ____ 25% ...
*March 21, 2013*