Two loudspeakers, A and B, are driven by the same amplifier and emit sinusoidal waves in phase. The frequency of the waves emitted by each speaker is 641Hz . You are standing between the speakers, along the line connecting them and are at a point of constructive interference.How far must you walk toward speaker B to move to reach the first point of destructive interference?
Take the speed of sound to be 344 .

Answers

Answer 1

Answer:

Final answer:

You must walk approximately 0.2685 m, or 26.85 cm, towards speaker B to encounter the first point of destructive interference. This calculation is arrived at by determining the half-wavelength of the sound wave.

Explanation:

Interference occurs when two sound waves from the same source meet. When they constructively interfere, their amplitudes add together creating a louder sound, while when they destructively interfere, they cancel each other out creating a point of silence. Since you are initially in a position of constructive interference, you need to move towards speaker B at a distance that would change the path length difference to be equivalent to a half wavelength.

To find this distance, we first need to find the wavelength from the frequency. The formula for this is:

Wavelength = Speed of sound / Frequency

Given the speed of sound is 344 m/s and the frequency is 641 Hz, we find the wavelength to be roughly 0.537 m. A half wavelength, which characterizes the distance needed for destructive interference from total constructive interference, would then be 0.2685 m.

You must walk approximately 0.2685 m, or 26.85 cm, towards speaker B to encounter the first point of destructive interference.

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Answer 2

Answer:

Final answer:

To find the distance at which the first point of destructive interference occurs, divide the wavelength by 2. In this case, the distance is approximately 0.268 meters or 26.8 centimeters. Therefore, you would need to walk about 26.8 centimeters toward speaker B to reach the first point of destructive interference.

Explanation:

To determine the distance at which the first point of destructive interference occurs, we need to understand the concept of interference and the conditions for constructive and destructive interference. Constructive interference occurs when the waves from both speakers are in phase and add up to create a larger amplitude. Destructive interference occurs when the waves from both speakers are out of phase and cancel each other out, resulting in a smaller amplitude. In this case, since the speakers are emitting waves in phase, the distance at which destructive interference occurs is equal to half the wavelength of the waves.

The wavelength of a wave can be calculated using the formula:
Wavelength = Speed of sound / Frequency

In this case, the frequency is given as 641 Hz and the speed of sound is given as 344 m/s. Plugging in these values into the formula, we get:
Wavelength = 344 m/s / 641 Hz

Solving this, we find that the wavelength is approximately 0.536 meters. To find the distance to the first point of destructive interference, we divide the wavelength by 2:
Distance to first point of destructive interference = Wavelength / 2

Plugging in the calculated wavelength, we get:
Distance to first point of destructive interference = 0.536 meters / 2

Simplifying, we find that the distance is approximately 0.268 meters or 26.8 centimeters. Therefore, you would need to walk about 26.8 centimeters toward speaker B to reach the first point of destructive interference.

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Dr. John Paul Stapp was a U.S. Air Force officer who studied the effects of extreme acceleration on the human body. On December 10, 1954, Stapp rode a rocket sled, accelerating from rest to a top speed of 282 m/s (1015 km/h) in 5.2 s and was brought jarringly back to rest in only 1 s. Calculate his (a) magnitude of acceleration in his direction of motion and (b) magnitude of acceleration opposite to his direction of motion. Express each in multiples of g (9.80 m/s2) by taking its ratio to the acceleration of gravity. g g

Answers

Answer:

a = 5.53 g , a = -15g

Explanation:

This is an exercise in kinematics.

a) Let's look for the acceleration

as part of rest v₀ = 0

v = v₀ + a t

a = v / t

a = 282 / 5.2

a = 54.23 m / s²

in relation to the acceleration of gravity

a / g = 54.23 / 9.8

a = 5.53 g

b) let's look at the acceleration to stop

va = 0

0 = v₀ -2 a y

a = vi / y

a = 282/2 1

a = 141 m /s²

a / G = 141 / 9.8

a = -15g

Using an argument based on the general form of the Schrödinger equation, explain why if \psi (x) is a solution to the Schrödinger equation, then A\psi(x) must also be a solution if A is a constant.I saw an explanation for this from another posted question, but this person put the explanation in numerical/equation form. Is there any way someone can explain the answer to this question in words (NON numerical/equation form)?

Answers

From a mathematical point of view, the Schrödinger Equation is a LINEAR partial differential equation, as is a partial differential equation that is defined by a linear polynomial in the solution and its derivatives.

For a linear differential equation, if you got two different solutions $\psi$ and $\phi$ , then the linear combination $\alpha \psi + \beta \phi$ , where $\alpha$ and $\beta$ are scalars, is also a solution.

This also is valid for only one solution (think of the other solution as equal to zero, $\phi = 0$ ). So, as the Schrödinger Equation is a Linear partial differential equation, then if $\psi$ is a solution, then $A \psi$ must also be a solution.

This is extremely important for physicist, as let us know that the superposition principle is valid.

Determine whether the following statements are true and give an explanation or counterexample.(A) If the acceleration of an object remains constant, its velocity is constant.
(B) If the acceleration of object moving along a line is always 0, then its velocity is constant.
(C) It is impossible for the instantaneous velocity at all times a(D) A moving object can have negative acceleration and increasing speed.

Answers

Answer:

Explanation:(A)if a body is accelerating then it's velocity can't be constant since an object is said to be accelerating if it is changing velocity (B)if the acceleration of an object moving along a line is 0 then it's velocity will be constant since there is no change in direction or speed(C)No.it is not possible for a moving body to have an instantaneous velocity at all times since instantaneous velocity is the velocity of a body at a certain instant of time..(D)Yes a moving object can have a negative acceleration and increasing speed,it can also have a positive acceleration with decreasing speed.

Burns produced by steam at 100°C are much more severe than those produced by the same mass of 100°C water. Calculate the quantity of heat in (Cal or kcal) that must be removed from 6.1 g of 100°C steam to condense it and lower its temperature to 46°C. Specific heat of water = 1.00 kcal/(kg · °C); heat of vaporization = 539 kcal/kg; specific heat of human flesh = 0.83 kcal/(kg · °C).

Answers

Final answer:

To calculate the quantity of heat that must be removed from 6.1 g of 100°C steam, we need to consider both the change in temperature and the phase change from steam to liquid. The specific heat of water is used to calculate the heat required to lower the temperature, while the heat of vaporization is used to calculate the heat required to condense the steam. Adding these two heat values together gives us the total amount of heat that must be removed from the steam, which is approximately 3.61164 kcal.

Explanation:

When steam at 100°C condenses and its temperature is lowered to 46°C, heat must be removed from the steam. To calculate the amount of heat, we can use the specific heat of steam and the latent heat of vaporization. First, we calculate the heat required to lower the temperature of the steam from 100°C to 46°C using the specific heat of water. We then calculate the heat required to condense the steam using the latent heat of vaporization. Finally, we add these two heat values together to obtain the total amount of heat that must be removed from the steam.

Given:

Mass of steam = 6.1 g
Temperature change = 100°C - 46°C = 54°C
Specific heat of water = 1.00 kcal/(kg · °C)
Heat of vaporization = 539 kcal/kg

Calculations:

Heat required to lower the temperature of the steam:
Q1 = mass × specific heat × temperature change
= 6.1 g × (1.00 kcal/(kg · °C) ÷ 1000 g) × 54°C
Heat required to condense the steam:
Q2 = mass × heat of vaporization
= 6.1 g × (539 kcal/kg ÷ 1000 g)
Total heat required:
Q = Q1 + Q2

Calculation:

Q1 = 0.32874 kcal
Q2 = 3.2829 kcal
Q = Q1 + Q2 = 0.32874 kcal + 3.2829 kcal = 3.61164 kcal

Therefore, the quantity of heat that must be removed from 6.1 g of 100°C steam to condense it and lower its temperature to 46°C is approximately 3.61164 kcal.

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Final answer:

To condense and cool 6.1 g of 100°C steam to 46°C, 3.2879 kcal must be removed for condensation, and 0.3304 kcal for cooling, for a total of 3.6183 kcal.

Explanation:

Calculating the Quantity of Heat for Condensation and Cooling

To calculate the quantity of heat that must be removed from 6.1 g of 100°C steam to condense it and lower its temperature to 46°C, we need to consider two processes: condensation and cooling. For condensation, we use the heat of vaporization, and for cooling, we use the specific heat of water.

Calculate the heat released during condensation of steam into water at 100°C:
Heat = mass × heat of vaporization
Heat (in kcal) = (6.1 g) × (539 kcal/kg) × (1 kg / 1000 g)
Heat = 3.2879 kcal
Calculate the heat released when the water cools from 100°C to 46°C:
Heat = mass × specific heat × change in temperature
Heat (in kcal) = (6.1 g) × (1.00 kcal/kg°C) × (1 kg / 1000 g) × (100°C - 46°C)
Heat = 0.3304 kcal

Total heat removed is the sum of the heat from both steps: 3.2879 kcal + 0.3304 kcal = 3.6183 kcal.

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4 A wheel starts from rest and has an angular acceleration of 4.0 rad/s2. When it has made 10 rev determine its angular velocity.]

Answers

The rate of change of angulardisplacement is defined as angular velocity. The angular velocity will be 22.41rad/s.

What is angular velocity?

The rate of change of angular displacement is defined as angular velocity. Its unit is rad/sec.

ω = θ t

Where,

θ is the angle of rotation,

tis the time

ω is the angular velocity

The given data in the problem is;

u is the initialvelocity=0

α is the angularacceleration = 4.0 rad/s²

t is the time period=

n is the number of revolution = 10 rev

From Newton's second equation of motion in terms of angular velocity;

$\rm \omega_f^2 - \omega_i^2 = 2as \n\n \rm \omega_f^2 - 0 = 2* 4 * 62.83 \n\n \rm \omega_f= 22.41 \ rad/sec$

Hence the angular velocity will be 22.41 rad/s.

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Answer:

$w_f$ = 22.41rad/s

Explanation:

First, we know that:

a = 4 rad/s^2

S = 10 rev = 62.83 rad

Now we know that:

$w_f^2-w_i^2=2aS$

where $w_f$ is the final angular velocity, $w_i$ the initial angular velocity, a is the angular aceleration and S the radians.

Replacing, we get:

$w_f^2-(0)^2=2(4)(62.83)$

Finally, solving for $w_f$ :

$w_f$ = 22.41rad/s

A beam of light travels from a medium with an index of refraction of 1.27 to a medium with an index of refraction of 1.46. If the incoming beam makes an angle of 14.0° with the normal, at what angle from the normal will it refract?