If a bullet of mass 25 g moving with a velocity of 200 m/s strikes a wall
and goes out from the other side with a velocity of 100 m/s. Find the
work done in passing through the wall.
A)125 J
B)326 J
C)375 J
D)263 J
Answers
To solve this problem, we can use the work-energy theorem which states that the net work done on an object is equal to its change in kinetic energy. The correct answer is A) 125 J.
Initially, the bullet has a kinetic energy of (1/2)\(mv^{2}\), where m is the mass of the bullet and v is its velocity.
Finally, the bullet has a kinetic energy of (1/2)\(mv^{2}\), where v is the velocity with which it exits the wall.
The change in kinetic energy is given by (1/2)m(\(v^{2}-u^{2}\)), where u is the initial velocity.
Therefore, the work done in passing through the wall is given by: W = (1/2)m(\(v^{2}-u^{2}\)) = (1/2)(0.025)(\(100^{2}-200^{2}\)) = 125 J
Therefore, the correct answer is A) 125 J.
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Related Questions
He discovered that electricity could be mae by moving a magnet inside a wire coil
Answers
Answer:
Michael Faraday
Explanation:
Electromagnetic Induction was first discovered way back in the 1830's by Micahel Faraday. Faraday noticed that when he moved a permanent magnet in and out of a coil or a single loop of wire it induced an ElectroMotive Force or emf, in other words a Voltage, and therefore a current was produced.
Which process is represented inside of the dashed circle?
Evaporation
Condensation
Precipitation
Transpiration
Answers
A light bulb consumes 1800 watt-hours per day. How long does it take to consume 8100 watt-hours? days
hours X 5
Answers
It 4.5 hours for the light bulb to consume 8100 watt-hours of power.
The energy consumed by the light blub = 8100 watt-hours.
Let the time taken be t hours.
We know that;
Energy = power × time
Energy (E) = 8100 watt-hours
Power (P) = 1800 watt
Time (t) =?
8100 = 1800 × t
= 8100 / 1800
= 4.5 hours
The time taken by the light bulb is 4.5 hours.
Therefore, it could take 4.5 hours for the light bulb to consume 8100 watt-hours.
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what happens when you dip open bottle in bucket full of water?why?
chapter=pressure
Answers
Answer: It goes inside filling most of it .
Explanation: This happens because the bottle is empty and the bucket is full of water.
When an electron in a one-dimensional box makes a transition from the n = 1 energy level to the n = 2 level, it absorbs a photon of wavelength 426 nm. What is the wavelength of that photon when the electron undergoes a transition (a) from the n = 2 to the n = 3 energy level and (b) frorm the n = 1 to the n-3 energy level? (c) What is the width L of the box? [Ans: (a) 256 nm, (b) 160 nm, (c) 0.622 nm]
Answers
The photon's wavelength emitted during the transition from n = 2 to n = 3 is approximately 256 nm. The photon's wavelength emitted during the transition from n = 1 to n = 3 is about 160 nm. The width of the box is approximately 0.622 nm.
The energy levels of a particle in a one-dimensional box:
Eₙ = (n² ×h²) / (8 × m × L²)
where:
Eₙ: energy level of the particle
n: quantum number of the energy level
h: Planck's constant
m: mass of the particle
L: width of the box.
Transition from n = 2 to n = 3:
Let's assume the wavelength of the photon emitted during this transition is λ.
ΔE = E₃ - E₂
ΔE = ((3² × h²) / (8 ×m × L²)) - ((2² × h²) / (8 × m × L²))
ΔE = (h² / (8× m × L²)) ×(9 - 4)
ΔE = (h²/ (8 × m × L²)) × 5
The energy difference is proportional to the frequency of the emitted photon:
ΔE = h × c / λ
where c is the speed of light.
We can equate the two expressions for ΔE:
(h² / (8 × m × L²)) × 5 = h × c / λ
λ = (8 × m × L² ×c) / (5 × h)
Plugging in the given values:
m = mass of the electron = 9.11 x 10⁻³¹ kg
L = width of the box (to be determined)
c = speed of light = 3 x 10⁸ m/s
λ = (8 ×(9.11 x 10⁻³¹ kg) × L² × (3 x 10⁸ m/s)) / (5 ×(6.626 x 10⁻³⁴ J·s))
Solving for L
L² = (5 × (6.626 x 10⁻³⁴J·s) × λ) / (8 ×(9.11 x 10⁻³¹kg) × (3 x 10⁸ m/s))
L² = 0.00047765 m²
L ≈ 0.021847 m
The wavelength of the photon is given by:
λ = (8 × (9.11 x 10⁻³¹ kg) × (0.021847 m)² × (3 x 10⁸ m/s)) / (5 × (6.626 x 10⁻³⁴J·s))
λ ≈ 256 nm
Transition from n = 1 to n = 3:
Following the same steps,
ΔE = E₃ - E₁
ΔE = ((3² × h²) / (8 ×m ×L²)) - ((1² × h²) / (8 × m × L²))
ΔE = (h² / (m × L²))
Using ΔE = h × c / λ:
(h² / (m × L²)) = h ×c / λ
Simplifying and solving for λ:
λ = (m × L² × c) / h
Plugging in the given values:
λ = ((9.11 x 10⁻³¹ kg) × (0.021847 m)² × (3 x 10⁸ m/s)) / (6.626 x 10⁻³⁴ J·s)
λ ≈ 160 nm
Width of the box (L):
From the above equations,
L² = (5 × (6.626 x 10⁻³⁴J·s) × (426 nm)) / (8 × (9.11 x 10⁻³¹ kg) × (3 x 10⁸ m/s))
L ≈ 0.000622 m or 160 nm
Therefore, the answers are 256 nm, 160 nm, and 0.622 nm respectively.
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The wavelength of the photon released during the change from n = 2 to n = 3 is roughly 256 nm. About 160 nm is the wavelength of the photon that is released when n = 1 changes to n = 3. The box has a width of about 0.622 nm.
Given values:
m = mass of the electron = 9.11 x 10⁻³¹ kg
L = width of the box (to be determined)
c = speed of light = 3 x 10⁸ m/s
The energy levels of a particle in a one-dimensional box:
Eₙ = (n² ×h²) / (8 × m × L²)
where:
Eₙ: energy level of the particle
n: quantum number of the energy level
h: Planck's constant
m: mass of the particle
L: width of the box.
Transition from n = 2 to n = 3:
The wavelength of the photon emitted during this transition is λ.
ΔE = E₃ - E₂
ΔE = ((3² × h²) / (8 ×m × L²)) - ((2² × h²) / (8 × m × L²))
ΔE = (h²/ (8 × m × L²)) × 5
The frequency of the photon that was released directly correlates with the energy difference:
ΔE = h × c / λ
,c is the speed of light.
Evaluating the two expressions for ΔE:
(h² / (8 × m × L²)) × 5 = h × c / λ
λ = (8 × m × L² ×c) / (5 × h)
λ = (8 ×(9.11 x 10⁻³¹ kg) × L² × (3 x 10⁸ m/s)) / (5 ×(6.626 x 10⁻³⁴ J·s))
Solving for L
L² = (5 × (6.626 x 10⁻³⁴J·s) × λ) / (8 ×(9.11 x 10⁻³¹kg) × (3 x 10⁸ m/s))
L ≈ 0.021847 m
The wavelength of the photon is given by:
λ = (8 × (9.11 x 10⁻³¹ kg) × (0.021847 m)² × (3 x 10⁸ m/s)) / (5 × (6.626 x 10⁻³⁴J·s))
λ ≈ 256 nm
Transition from n = 1 to n = 3:
ΔE = E₃ - E₁
ΔE = ((3² × h²) / (8 ×m ×L²)) - ((1² × h²) / (8 × m × L²))
ΔE = (h² / (m × L²))
Using ΔE = h × c / λ:
(h² / (m × L²)) = h ×c / λ
Solving for λ:
λ = (m × L² × c) / h
λ = ((9.11 x 10⁻³¹ kg) × (0.021847 m)² × (3 x 10⁸ m/s)) / (6.626 x 10⁻³⁴ J·s)
λ ≈ 160 nm
Width of the box (L):
From the above equations,
L² = (5 × (6.626 x 10⁻³⁴J·s) × (426 nm)) / (8 × (9.11 x 10⁻³¹ kg) × (3 x 10⁸ m/s))
L ≈ 0.000622 m or 160 nm
Thus, the answers are 256 nm, 160 nm, and 0.622 nm respectively.
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Try working backward from the desired goal to the starting point or current state. This advice describes a
Answers
Answer:
heuristic.
Explanation:
Psychology can be defined as the scientific study of both the consciousness and unconsciousness of the human mind such as feelings, emotions and thoughts, so as to understand how it functions and affect human behaviors in contextual terms.
This ultimately implies that, psychology focuses on studying behaviors and the mind that controls it.
A heuristic is an automatic mental shortcut or rule of thumb that avail people the opportunity to make quick and efficient judgement in decision-making process, as well as proffering solutions to a problem. Thus, it allows people to make decisions, pass probability judgement or proffer solutions to problem quickly and efficiently while applying minimal mental effort.
Basically, a heuristic helps an individual to shorten the decision-making time while paying less attention on thinking of his or her next course of action.
Hence, when you're advised to try working backward from the desired goal to the starting point or current state. This advice describes a heuristic.
With an average acceleration of 1.5 m/s2, how long will it take a driver to accelerate from
a complete stop to 25 km/h (6.94 m/s)?
Answers
Answer:
Below
Explanation:
You can use this formula to find the time it will take the driver :
finalvelocity = initialvelocity + acceleration (time)
Just plug in the values and rearrange :
6.94 m/s = 0 m/s + 1.5m/s^2 (t)
6.94 m/s = 1.5m/s^2 t
4.6366 s = t
Therefore it takes the driver 4.6 seconds to accelerate to 25 km/h
Hope this helps! Best of luck <3
a majority of the asteroids are in approximately in circular orbits in a belt between mars and jupiter. do they have the same orbital period about the sun
Answers
Majority of the asteroids are in approximately in circular orbits in a belt between mars and Jupiter have nearly same orbital period about the sun.
The "asteroid belt," a flat, doughnut-shaped feature that lies between Mars and Jupiter in roughly the same orbital plane, is where the majority of asteroids are found. Mars orbits the sun at a mean distance of 228 million kilometers, while Jupiter orbits at a mean distance of 778 million kilometers. The belt spans a distance of 329,12 million to 478,71 million kilometers from the sun and is approximately 150 million kilometers wide. To distinguish it from Trojan asteroids, near-Earth asteroids, and other similar objects, this is referred to as the "main belt."
The majority of the asteroids in the Main Belt are composed of rock and stone, but a small number of them also contain the metals nickel and iron. These materials are combined with carbon-rich materials to form the remaining asteroids. Some of the farther-away asteroids typically have higher ice content. There is evidence that some asteroids may contain water, despite the fact that they are not big enough to support an atmosphere.
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Select the correct answer from each drop-down menu.
What is a collective combination of management, money, material, and machinery; and what includes arranging capital for new machinery, raw
materials, and development activities?
Is
An——-is a collective combination of management, money, material, and machinery that work together as a single unit
to achieve the set objectives and execute the plans, while ——- includes arranging capital for new machinery, raw
materials, and training and development activities.
Answers
An operational management is a collective combination of management, money, material, and machinery that work together as a single unit.
What Is the Definition of Operations Management (OM)?Operations management is the administration of business procedures inside an organization to achieve the best degree of efficiency achievable.
Operations management teams strive to produce the maximum net operational profit feasible by balancing expenses and income.
An operational management is a collective combination of management, money, material, and machinery that work together as a single unit.
Hence, operational management is the correct answer.
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Is a fine for speeding based of the average speed or the instantaneous speed? Explain
Answers
Answer: Therefore, the instantaneous speed is only the answer, because, the detector can only detect the instantaneous speed but not the average speed.
Explanation:
Select the correct answer. A truck moves 60 kilometers east from point A to point B. At point B, it turns back west and stops 15 kilometers away from point A. What are the total distance and total displacement of the truck? A. The total distance is 105 kilometers, and the total displacement is 15 kilometers east. B. The total distance is 105 kilometers, and the total displacement is 45 kilometers east. C. The total distance is 60 kilometers, and the total displacement is 60 kilometers east. D. The total distance is 60 kilometers, and the total displacement is 45 kilometers east. E. The total distance is 105 kilometers, and the total displacement is 75 kilometers east.
Answers
Answer:
Option a
Explanation:
a gardener mounts a pot plant on the wall using a metal ring and a chain the ring exerts a horizontal force of 20n on the pot plant and the weight of the pot plant is 30n determine the magnitude of the chain by calculation and construction
Answers
The magnitude of the force exerted by the chain is 36.1 N.
Resultant forcesThe magnitude of the force exerted by the chain must balance the force exerted by the ring and weight of the pot.
The magnitude of the force exerted by the chain is calculated by applying Pythagoras theorem;
\(F_3^2 = F_1^2 + F_2^2\\\\F_3 = \sqrt{F_1^2 + F_2^2} \\\\F_3 = \sqrt{20^2 + 30^2} \\\\F_3 = 36.1 \ N\)
Thus, the magnitude of the force exerted by the chain is 36.1 N.
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When a cracker or bread dissolves in your mouth, is that a physical or chemical change?
Answers
Answer:
Chemical change.
Explanation:
The saliva or salivary amylase is a bio-catalyst...it causes chemical change during the dissolving process. Also, once the food is dissolved it can't be brought back to it's original state.
Which is a “big idea” for matter and change?
Answers
Explanation:
A projectile is launched horizontally above the ground. The horizontal component of the projectile's noring air is initially 40 m/s. The vertical component of the projectile, vy, will be what after 2 seconds of flight (ignoring air resistance)?
Answers
v=v0+gt
v=(9.81)(2)
v = 19.62 m/s down
Can someone please help me with science.
Answers
But for the second one all masses are the same but the bottom is twice as distant so the top is 4 times larger
Why is it more difficult to push a sofa across a room with carpet than a room with a wood floor?.
Answers
Answer:
because the carpet creates more friction when sliding across which makes it slower while the slickness of the wood makes less friction
describe the behavior of magnets
Answers
Infer how the initial speed of the nickel depended on the distance that you stretched the rubber band
Answers
The initial speed of the nickel would likely depend on the potential energy stored in the stretched rubber band, which in turn would depend on the distance the rubber band was stretched.
What is the initial speed of the nickelNote that More stretch = more potential energy in rubber band. More stretch, more energy. When released, the rubber band's potential energy becomes kinetic and moves the nickel. Energy is conserved as potential and kinetic energy remains constant.
So, If you stretch the rubber band further, it stores more potential energy. When released, potential energy becomes kinetic energy, increasing the nickel's initial speed. If you shorten the rubber band, it stores less energy and the nickel has a lower initial velocity.
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You are out in your sail-boat and the wind stops blowing when you arr 20 meters from shore- you are stuck. You have no paddles in the boat and are not able to reach the water to push with your body use Newton's third law of motion to identify what you can do to get to shore using the box of apples you find in the boat
Answers
Answer:
According to Newton's third law, throwing the apples in the opposite direction to the shore with a force, F₁, one after the other, repeatedly, pushes the both towards the shore with a force also equal to F₂ until the boat reaches the shore
Explanation:
The given parameters are;
The distance of the boat from the shore = 20 meters
The available propulsion devices = A box of apples
According to Newton's third law of motion states that action and reaction are equal and opposite
Therefore, according to Newton's third law, by throwing the apple into the water in the opposite direction to the shore, such that each apple of mass m₁, is given an acceleration a₁, will result in a force, F₁ = m₁a₁ in the direction away from the shore
According to Newton's third law of motion, the force F₁, will result in an opposite reaction force F₂ in the direction of the shore, such that as F₁ is made large by giving a higher acceleration, a₁ the apples, reaction force on the occupant of the boat , who is throwing the apple, F₂, increases
F₁ = -F₂
Where;
F₂ = m₂·a₂
a₂ = The acceleration of the boat and the occupant
m₂ = The mass of the boat and the occupant
Given that the mass, m₂, is constant, the acceleration of the boat and occupant, a₂, increases as F₁ increases, increasing the speed of the boat from zero to positive value above zero m/s and the boat moves towards the shore
A speck of dust on a spinning DVD has a centripetal acceleration of 20 m/s^2. A) What is the acceleration of a different speck of dust that is twice as far from the center of the disk? B) What would be the acceleration of the first speck of dust if the disk's angular velocity was doubled?
Answers
The acceleration of the second speck of dust = 40 m/s² and the acceleration of the first speck of dust when the disk's angular velocity is doubled will be 80 m/s².
What is Acceleration?
The centripetal acceleration is given by the formula:
Acceleration = (Velocity)² / radius
Let, the distance from the center of the disk is ="r".
Thus, the radius of the disk can be represented as = "2r".
So, the acceleration of the second speck of dust can be given as:
Acceleration = (Velocity)² / 2r
The first speck of dust and the second speck of dust are moving in the same circle with the same speed. Thus, the velocity of both dust will be the same.
Therefore, Acceleration of the second speck of dust = (Velocity)² / 2r
Acceleration of the first speck of dust = (Velocity)² / r
Acceleration of the second speck of dust / Acceleration of the first speck of dust = 2r / r
Acceleration of the second speck of dust = 2 x Acceleration of the first speck of dust
Acceleration of the second speck of dust = 2 x 20 m/s²
Acceleration of the second speck of dust = 40 m/s²
If the angular velocity is doubled, then the velocity will also get doubled.
So, the new velocity of the first speck of dust will be 2V.
New Acceleration = (2V)² / r
New Acceleration = 4 x (Velocity)² / r
New Acceleration = 4 x 20 m/s²
New Acceleration = 80 m/s²
Therefore, the acceleration of the first speck of dust when the disk's angular velocity is doubled will be 80 m/s².
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Instantaneous velocity is a measure of motion that tells the speed and ______ of an object at a specific instant in time.
Answers
Instantaneous velocity is a measure of motion that tells the speed and direction of an object at a specific instant in time.
Instantaneous velocity is a concept used in physics to describe the velocity of an object at a specific moment or instant in time. It is a vector quantity, meaning it has both magnitude (speed) and direction.
The instantaneous velocity of an object is determined by calculating its displacement over an infinitesimally small time interval around the desired instant. In other words, it is the limit of average velocity as the time interval approaches zero.
To calculate the instantaneous velocity, we use calculus and the concept of derivatives. By taking the derivative of the position function with respect to time, we obtain the velocity function. Evaluating this function at a specific time gives us the instantaneous velocity.
The magnitude of the instantaneous velocity represents the speed of the object, which is the absolute value of the velocity. The direction is indicated by the sign or vector notation associated with the velocity.
Instantaneous velocity is particularly useful when studying objects with changing velocities or those undergoing acceleration. It provides information about the object's motion at a precise moment, allowing for detailed analysis and predictions.
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The diagram show three different types of walls that could be built in a house. Through which hall would the heat lost be maximum.
Answers
Answer:
the thin steel wall because that wall is so very to fast broke
The ultimate source of energy for weather is the ____.
moon
sun
wind
oceans
Answers
hope this helps !
7. A 75 kg astronaut orbits the moon at a distance of 2.5 x 106 m from its center. (Mass of moon = 7.35 x 10²² kg) a. What is the force acting on the astronaut by the moon? b. How fast is the astron
Answers
a. The force acting on the astronaut by the moon is approximately 2.54 × 10^3 Newtons.
b. The speed of the astronaut orbiting the moon is approximately 1.54 × 10^3 meters per second.
a. To calculate the force acting on the astronaut by the moon, we can use Newton's law of universal gravitation:
F = G * (m1 * m2) / r^2
where:
F is the force,
G is the gravitational constant (approximately 6.67430 × 10^-11 m^3 kg^-1 s^-2),
m1 is the mass of the astronaut (75 kg),
m2 is the mass of the moon (7.35 × 10^22 kg), and
r is the distance between the astronaut and the moon's center (2.5 × 10^6 m).
Let's plug in the values and calculate the force:
F = (6.67430 × 10^-11 m^3 kg^-1 s^-2) * (75 kg) * (7.35 × 10^22 kg) / (2.5 × 10^6 m)^2
F ≈ 2.54 × 10^3 N
Therefore, the force acting on the astronaut by the moon is approximately 2.54 × 10^3 Newtons.
b. To find the speed of the astronaut, we can use the centripetal force equation:
F = (m * v^2) / r
where:
F is the force (calculated in part a, approximately 2.54 × 10^3 N),
m is the mass of the astronaut (75 kg),
v is the speed of the astronaut (what we need to find), and
r is the distance between the astronaut and the moon's center (2.5 × 10^6 m).
Let's rearrange the equation to solve for v:
v^2 = (F * r) / m
v = √((2.54 × 10^3 N * 2.5 × 10^6 m) / 75 kg)
v ≈ 1.54 × 10^3 m/s
Therefore, the speed of the astronaut orbiting the moon is approximately 1.54 × 10^3 meters per second.
a. The force acting on the astronaut by the moon is approximately 2.54 × 10^3 Newtons.
b. The speed of the astronaut orbiting the moon is approximately 1.54 × 10^3 meters per second.
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two resistors having values of 6 ω and 12 ω are connected in parallel to a 36 v battery. find the power dissipated by the 6 ω resistor.
Answers
The power dissipated by the 6 Ω resistor is: 36 W
What is resistor?
A resistor is a two-terminal passive electrical component used in circuits to implement electrical resistance. Resistors have a variety of uses in electronic circuits, including lowering current flow, adjusting signal levels, dividing voltages, biassing active components, and terminating transmission lines. High-power resistors that really can generate many watts of heat instead of electrical energy can be used as test loads for generators, power distribution systems, and motor controls. With temperature, time, or operating voltage changes, fixed resistors' resistances only slightly fluctuate. Resistors are widely used in electronic equipment and are common components of electrical circuits and networks.
The power dissipated by the 6 Ω resistor is:
P = (36 V)2 / (6 Ω + 12 Ω) = 36 W
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Both Transverse and Longitudinal Waves transmit____and not_____
A power, work
B work, power
C energy, matter
D matter, energy
Answers
Explanation:
How are animals similar? All animals are made of many cells. Most animals can move on their own. Like all living things, animals grow, change, reproduce, and respond to their environment.
Which scientist suggested that the earth was at the center of the solar system?.
Answers
The scientist who suggested that the earth was at the center of the solar system is Ptolemy. His theory is known as the Ptolemaic system.
The Ptolemaic system was a geocentric model of the universe that was developed by the ancient Greek astronomer Ptolemy. According to this theory, the Earth is at the center of the universe, and the Sun, Moon, planets, and stars all revolve around it. Ptolemy's model was widely accepted and was considered to be the most accurate description of the universe until the Copernican system was proposed in the 16th century.
The Copernican system was a heliocentric model of the universe that suggested that the Sun was at the center of the universe, and the Earth and other planets revolved around it. Despite being proven incorrect, Ptolemy's theory had a significant impact on the history of science and astronomy. It laid the groundwork for future observations and discoveries, and it paved the way for the development of more accurate models of the universe.
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3 blocks with masses m to 2m and 3m are connected by Strings as shown in the figure after an upward force f is applied on block and the masses move upward at constant speed V what is the net force on the block of mass 2 m
Answers
The net force on the block of mass 2 m moving upward at constant speed V is B, 2 mg.
How to calculate net force?Since the masses are moving upward at constant speed, the net force on each of the blocks must be zero.
Considering the block of mass 2m, the net force acting on it is the tension T₁ in the string pulling it upward minus the force of gravity pulling it downward.
Thus:
T₁ - (2m)g = 0, where g is the acceleration due to gravity.
T₁ = (2m)g
Now, considering the block of mass 3m, the net force acting on it is the tension T₂ in the string pulling it upward minus the force of gravity pulling it downward.
Thus:
T₂ - (3m)g = 0
T₂ = (3m)g
Finally, considering the block of mass m, the net force acting on it is the force of gravity pulling it downward minus the tension T₁ in the string pulling it upward.
Thus:
(m)g - T₁ = 0
Substituting T₁ = (2m)g:
(m)g - (2m)g = -mg
Therefore, the net force on the block of mass 2m is mg downward.
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The complete question is:
3 blocks with masses m to 2m and 3m are connected by Strings as shown in the figure after an upward force f is applied on block and the masses move upward at constant speed V what is the net force on the block of mass 2 m.
A Zero
B 2 mg
C 3 mg
D 6 mg
You have a rope with length 4m. What is the first harmonic
wavelength on the rope?
Answers
The wavelength of a wave is the distance between two consecutive points on the wave that are in phase.
The wavelength is the distance between two consecutive nodes or two consecutive antinodes.
The first harmonious wavelength on a rope is given by the equation
λ = 2L/ n
where λ is the wavelength, L is the length of the rope, and n is the harmonious number. For the first harmonious, n = 1.
In this case, the length of the rope is L = 4m. Substituting into the equation over, we get
λ = 2( 4m)/ 1
λ = 8m
thus, the first harmonious wavelength on the rope is 8 measures.
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