A butterfly is flying around and its velocity(v) as a function of time(t) is given in the graph below where rightwards is the positive velocity direction. What is the butterfly's displacement x from t=2 to 4s? Answer with two significant digits.
Answers
Answer: 19 meters.
Explanation:
We want to find the total displacement between t = 2s and t = 4s.
To do it, we can integrate our function, first write our velocity equation.
for t ≤ 3s, we have a linear equation, let's write it:
A linear relationship can be written as:
y = a*t + b
where a is the slope and b is the y-axis intercept.
For a line that passes through the points (x1, y1) and (x2, y2), the slope can be written as:
a = (y2 - y1)/(x2 - x1).
Now we can see that our line passes through the points (1, 0) and (0, -2)
then the slope is:
a = (0 -(-2)/(1 - 0) = 2/1 = 2
and knowing that when t = 0s, v(0s) = -2m/s, then our equation is:
v(t) = (2m/s^2)*t - 2m/s for t ≤ 3s
now, for t ≥3s the equation is constant, v(t) = 4m/s.
then we have
v(t) = (2m/s^2)*t - 2m/s -------if t ≤ 3s
v(t) = 4m/s ----- if t ≥ 3s
Now we integrate over time to get the position:
for t ≤ 3s we have:
p(t) = (1/2)*(2m/s^2)*t^2 - 2m/s*t + C
where C is a constant of integration, as we are calculating the displacement this constant actually does not matter, so we can use C = 0m
p(t) = (1m/s^2)*t^2 - 2m/s*t for t ≤ 3s
and p(3s) = (1m/s^2)*3s^2 - 2m/s*3s = 9m - 6m = 3m is the initial position of the other part of the function.
for t ≥ 3s we have:
p(t) = 4m/s*t + p(3s) = 4m/s*t + 3m
then the position equation is:
p(t) = (1m/s^2)*t^2 - 2m/s*t ---- t ≤ 3s
p(t) = 4m/s*t + 3m --- if t ≥ 3s
Now the displacement will be:
p(4s) - p(2s) where for each time, you need to use the correct function:
p(4s) = 4m/s*4s + 3m = 16m + 3m = 19m
p(2s) = (1m/s^2)*2s^2 - 2m/s*2s = 4m - 4m = 0m
p(4s) - p(2s) = 19m - 0m = 19m
The butterfly displacement x from t=2 to 4s is 19 meters.
What is displacement?The spacing between two specified points is represented by the one-dimensional quantity of displacement (symbolised as d or s), commonly known as length or distance.
The total displacement between t = 2s and t = 4s.
Integrate our function, the velocity equation.
for t ≤ 3s, we have a linear equation, let's write it:
A linear relationship can be written as:
y = a x t + b
where a is the slope and b is the y-axis intercept.
For a line that passes through the points (x1, y1) and (x2, y2), the slope can be written as:
a = (y2 - y1)/(x2 - x1).
The line passes through the points (1, 0) and (0, -2)
The slope is:
a = (0 -(-2)/(1 - 0) = 2/1 = 2
When t = 0s, v(0s) = -2m/s, then our equation is:
v(t) = (2m/s²) x t - 2m/s for t ≤ 3s
now, for t ≥3s the equation is constant, v(t) = 4m/s.
v(t) = (2m/s²) x t - 2m/s -------if t ≤ 3s
v(t) = 4m/s ----- if t ≥ 3s
Now we integrate over time to get the position:
for t ≤ 3s we have:
p(t) = (1/2) x (2m/s²) x t^2 - 2m/s x t + C
where C is a constant of integration, to calculate the displacement this constant actually does not matter,
p(t) = (1m/s²)*t^2 - 2m/s x t for t ≤ 3s
and p(3s) = (1m/s^2) x 3s² - 2m/s x 3s = 9m - 6m = 3m is the initial position of the other part of the function.
for t ≥ 3s we have:
p(t) = 4m/s x t + p(3s) = 4m/s x t + 3m
then the position equation is:
p(t) = (1m/s^2) x t² - 2m/s x t ---- t ≤ 3s
p(t) = 4m/s x t + 3m --- if t ≥ 3s
Now the displacement will be:
p(4s) - p(2s) where for each time, you need to use the correct function:
p(4s) = 4m/s x 4s + 3m = 16m + 3m = 19m
p(2s) = (1m/s²) x 2s²- 2m/s x 2s = 4m - 4m = 0m
p(4s) - p(2s) = 19m - 0m = 19m
Thus, the displacement is 19 m.
To learn more about displacement, refer to the link:
https://brainly.com/question/11934397
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Related Questions
(8.86 + 1.0 x 10^-3)÷3.610×10^-3
Answers
Answer:
2454.57
Explanation:
Step 1: Solve
[tex]\frac{(8.86+0.001)}{(3.610)(10^{-3}) }[/tex]
[tex]\frac{8.861}{0.003.61 }[/tex]
2454.57
Therefor the answer to this equation is 2454.57
A fire cracker is fired and it rises to a height of 1000 m. Find the velocity by which it was
released and the time taken by it to reach the highest point (take a = 10 m/s²).
Answers
Answer:
Explanation:it is too easy
A box with mass of 2 kg is pushed directly horizontally over a horizontal surface (with friction) at a constant speed of 10 m/s. The force of the push is 60 N. How much thermal energy is generated pushing the box a distance of 15 m
Answers
Answer:
E= 600 W
Explanation:
Given that
m = 2 kg
Speed , v= 10 m/s
Force , F= 60 N
Given that box is moving with constant velocity, it means that friction force will be 60 N.
f = 60 N
Therefore total energy generated
E= f x v
E= 60 x 10 = 600 W
E= 600 W
Thus the answer will be 600 W.
(02.10 LC)
Which American sport stems from a combination of the British sports rugby and soccer?
Baseball
Basketball
Tennis
Football
Question 2 Multiple Choice Worth 5 points)
Answers
Answer:
football
Explanation:
I took the 2.10 quiz and got it wrong so it must be football
Calculate the volume of this regular solid. A cylinder labeled B at the top, 13 centimeters high with a radius of 4 centimeters. What is the volume of the cylinder? Round your answer to the nearest hundredth.
Answers
Answer:
The volume of the cylinder is [tex]653.71\ \text{cm}^3[/tex]
Explanation:
Given that,
The height of the cylinder is 13 cm
Radius of the cylinder is 4 cm
We need to find the volume of the cylinder. The formula that is used to find the volume of a cylinder is given by :
[tex]V=\pi r^2 h\\\\V=\dfrac{22}{7} \times (4)^2 \times 13\\\\V=653.71\ \text{cm}^3[/tex]
So, the volume of the cylinder is [tex]653.71\ \text{cm}^3[/tex]
Answer:
653.45 is the answer
Explanation:
Use the diagram to answer each question.
Why might a researcher further classify the data in the chimpanzee dier table to include separate information of males and females ?
Answers
Answer:
In the data table, we can see the frequency distribution in the diet of a given type of chimpanzee.
Why a researcher further classify the data separating information of males and females?
Well, the objective of the researcher is to find information about these chimpanzees, so if he notices that the diet varies (even slightly) between males and females, separating the information between males and females would be useful to know how the diet varies, and why this happens.
This is the primary motive of why a researcher would want to separate the information of males and females.
plz help
I need it fast
Answers
Answer:
perpendicular to
Explanation:
it means perpendicular to .....should u come across something like this / / , this one means parallel to .....
Answer:
perpendicular
Explanation:
Some of the most popular symbols are:
Heart symbol: this represents love, compassion and health.
Dove symbol: this represents peace, love, and calm.
Raven symbol: this represents death and doom.
Tree symbol: this represents growth, nature, stability, and eternal life.
Owl symbol: this represents wisdom and intelligence.
A hammer is used to hit a nail into a board. Which statement is correct about the forces at play between the nail and the hammer? The nail exerts an equal force on the hammer in the same direction. The nail exerts a much smaller force on the hammer in the opposite direction. The nail exerts an equal force on the hammer in the opposite direction. The nail exerts a much smaller force on the hammer in the same direction.
Answers
Answer:
The nail exerts an equal force on the hammer in the opposite direction.
Explanation:
The Newtons third law states that there is an equal an opposite reaction for every action. When hammer pushes the nail, the nail will push the hammer back in opposite direction. When the hammer hits a nail then nail will exert the equal and opposite force to the hammer. These both objects will exert force on each other in opposite directions.
Hello, I am BrotherEye
Answer:
Answers are
1. "The nail exerts an equal force on the hammer in the opposite direction."
2. "500 N"
3. "The iron piece exerts a force of 1 N on the magnet in the opposite direction."
4. "When mass moves closer to the point of rotation, rotational inertia decreases."
5. "The skater spins slower because his rotational inertia has increased."
Explanation:
what is the symbol of mecury
Answers
If you are talking about mecury as in a chemical element than it is: Hg
If you are talking about the planet Mercury than: The symbol for Mercury represents the head and winged cap of Mercury, god of commerce and communication, surmounting his caduceus (staff). The symbol for Venus is designated as the female symbol, thought to be the stylized representation of the hand mirror of this goddess of love.
Answer:
The symbol of mercury is....
Hydrargyrum ( Hg )
Hope this helps......
Pls mark my ans as brainliest
How much work is done in moving a body of mass 1.0 kg from an elevation of 2 m to
an elevation of
Answers
Answer:
The work done is -176.4 J.
Explanation:
Given that,
Mass = 1.0 kg
An elevation of 2 m to an elevation of 20 m.
Suppose, Find the work done by the gravitational field of the earth?
We need to calculate the force
Using formula of force
[tex]F=mg[/tex]
Put the value into the formula
[tex]F=1.0\times9.8[/tex]
[tex]F=9.8\ N[/tex]
We need to calculate the displacement
Using formula of displacement
[tex]Displacement = s_{2}-s_{1}[/tex]
[tex]s=20-2=18\ m[/tex]
The direction of displacement is upward.
Since gravitational force is downwards and displacement is upwards,
Then the angle is 180°.
We need to calculate the work done
Using formula of work
[tex]W=f\cdos s\cos\theta[/tex]
[tex]W=9.8\times18\cos180[/tex]
[tex]W=-176.4\ J[/tex]
Hence, The work done is -176.4 J.
A wave has a frequency of 5 Hz and a wavelength of 0.5 m, what is the speed of this wave?
Answers
Answer:
2.5 m/s
Explanation:
The speed of a wave can be found using the following formula.
v= λ * f
where λ is the wavelength in meters (m) and f is the frequency of the wave in Hertz (Hz).
We know the wavelength is 0.5 m and the frequency of the wave is 5 Hz.
Therefore,
λ= 0.5 m
f = 5 Hz
v= 0.5 * 5
Multiply 0.5 by 5, or divide 5 by 2.
0.5 * 5= 2.5 or 5/2=2.5
v= 2.5
Add appropriate units. The units for wave speed are m/s (meters per second).
v= 2.5 m/s
The speed of the wave is 2.5 meters per second.
Which example best describes a restoring force?
any force that is applied to a spring to change its length
the force applied to stretch a spring and increase its length
the force applied to restore a spring to its original length
the force applied to compress a spring and shorten its length
Answers
Answer:
the force applied to restore a spring to its original length
Explanation:
a bird statue with a mass 0.2 kg hangs from a rubber band with spring constant 30 N/m.How much is the rubber band stretched when the statue hangs motionless
Answers
Answer:
Distance : 0.06533 meters or 65.33 mm
Explanation:
To solve this problem we can make the forces equal when the system is at equilibrium.
mass [tex]*[/tex] gravity ( constant ) = spring constant
where l = the length at which the rubber band is stretched
0.2 kg [tex]*[/tex] 9.8 m / s² = 30 N/m
1.96 kg [tex]*[/tex] m / s² = 30 N/m
l = 1.96 kg [tex]*[/tex] m / s² / 30 N/m = 0.06533 meters / 65.33 mm
The rubber band is stretched a distance of 0.06533 meters, or 65.33 mm.
Answer:
0.065
Explanation:
Apex i just got it right
If a gas and a liquid are both at the same temperature, the particles of gas have a higher average kinetic energy. True or false?
Answers
Answer:
True
Explanation:
The average kinetic energy is the measure of how freely the molecules of a substance moves relative to the other molecules within the substance. Gas and liquids are together termed fluids, but the molecules of a gas naturally has more more average kinetic energy that that of a liquid, if they are kept at the same temperature. This explains why gases are easy to expand, and have to be confined by a container. So the particles of a gas has more kinetic energy that that of a liquid even if they are kept at the same temperature.
Pls help A car starts from rest and gains a velocity of 20m/s in 10 seconds calculate its acceleration and the distance covered by it in this time
Answers
Answer:
[tex] \boxed{\sf Acceleration \ (a) = 2 \ m/s^{2}} [/tex]
[tex] \boxed{\sf Distance \ covered \ (s) = 100 \ m} [/tex]
Given:
Initial velocity (u) = 0 m/s
Final velocity (v) = 20 m/s
Time taken (t) = 10 sec
To Find:
(i) Acceleration (a)
(ii) Distance covered (s)
Explanation:
[tex]\sf (i) \ From \ 1^{st} \ equation \ of \ motion:[/tex]
[tex] \sf \implies v = u + at[/tex]
[tex] \sf \implies 20 = 0 + a(10)[/tex]
[tex] \sf \implies 10a = 20[/tex]
[tex] \sf \implies \frac{10a}{10} = \frac{20}{10} [/tex]
[tex] \sf \implies a = 2 \: m/ {s}^{2} [/tex]
[tex]\sf (ii) \ From \ 2^{nd} \ equation \ of \ motion:[/tex]
[tex] \sf \implies s = ut + \frac{1}{2} a {t}^{2} [/tex]
[tex]\sf \implies s = (0)(10) + \frac{1}{2} \times 2 \times {(10)}^{2} [/tex]
[tex]\sf \implies s = \frac{1}{ \cancel{2}} \times \cancel{2} \times {(10)}^{2} [/tex]
[tex]\sf \implies s = {10}^{2} [/tex]
[tex]\sf \implies s = 100 \: m[/tex]
In series combination of resistors, the total electric current is equal to the current flowing through each resistor.
A. False B. True C.The statement above lacks information
WILL GIVE BRAINLIEST! :)
Answers
Answer:
The answer is B, true.
Because same current flows through each resistors in Series.
Plz Mark as Brainlist
And follow me.
[tex] \LARGE{ \underline{ \tt{ \pink{True \: or \: False}}}}[/tex]
The above statement is true.
❍ In series combination of resistors, the total electric current is equal to the current flowing through each resistor..
Explanation:-In series combination, the resistors are connected end to end.There is no branch of extra wire with resistor, Hence Current through the entire circuit remains constant.The Potential difference between the resistors changes due to variation in end points. The equivalent resistance of the total circuit is the sum of the resistors connected end to end.The total or equivalent resistance is always greater than other individual resistance.━━━━━━━━━━━━━━━━━━━━
Identify the wood turning equipment and what it does.
А
is used to turn wood. It rotates and carves wood to produce a
form.
Answers
Answer:
lathe
perfectly symmetrical
Answer: A lathe is used to turn wood . It rotates and carves wood to produce a perfectly symmetrical form .
First one is lathe .
Second one is perfectly symmetrical .
Explanation: I just took the test on Plato and had 100%
A person holds a 25 kg (250 newton) bag of cement over his head and moves it a distance of 10 m, taking 2 minutes, while another person carries it on a wheelbarrow that same distance, taking 1 minute.Who does more work ? What is the power of each person?
Answers
Explanation:
Assuming the 10 m distance is the vertical displacement, the work done by both people is the same.
Work = force × distance
W = (250 N) (10 m)
W = 2500 J
The power of the first person is:
Power = work / time
P = 2500 J / 120 s
P = 20.83 W
The power of the second person is:
P = 2500 J / 60 s
P = 41.67 W
a ferris wheel has a centripetal acceleration equal to 2m/s squared. what is the centripetal force acting on a 45 kg boy riding in one of the cars when the car is on the top of the ferris wheel? what is the force exerted by the seat on the boy when the car is at the top of the ferris wheel
Answers
Explanation:
[tex]centripetal \: force = \frac{m {v}^{2} }{r} [/tex]
Centripetal force = 45 * 2 = 90 N
Therefore, centripetal force acting on a 45 kg boy riding in one of the cars when the car is on the top of the ferris wheel is 90 N.
The force exerted by the seat on the boy when the car is at the top of the ferris wheel is a centrifugal (pseudo force) acting (since the since the seat is in non- inertial frame) in exact opposite direction (Outwards) as the centripetal force and is equal in magnitude.
A stone of 1 kg is thrown with a velocity of 40 m/s across the frozen surface of a lake and comes to rest after travelling a distance of 50 m. What is the force of friction between the stone and the ice? *
A)16 N
B)-4 N
C)-16 N
Answers
Answer:
C)-16 N
Explanation:
concepts used
force = mass* acceleration
equation of motion
[tex]v^2 = u^2 + 2as[/tex]
where v is the final velocity
u is the initial velocity
and s is the distance moved
______________________________________________
Given
mass = 1 kg
initial velocity (u) = 40m/s
final velocity (v) = 0 as stones comes to rest
distance moved by stone (s) = 50m
using [tex]v^2 = u^2 + 2as[/tex]
[tex]0 = 40^2 +2a*50\\=> -1600 = 100a\\=> a = -1600/100 = -16[/tex]
Thus, acceleration is -16 m/s^2
here acceleration is negative as force of friction is opposing the motion.
Force of friction = mass of stone * acceleration of stone
Force of friction = 1*-16 kgm/s^2 = -16N ( kgm/s^2 = 1 N)
Thus, option c -16N is correct choice.
The marginal cost curve
(a) Lies below the ATC curve when the ATC curve slopes upward.
(b) Intersects the AFC and ATC curves at their respective minimum points.
(c) Lies above the AVC curve when the AVC curve slopes downward.
(d) Intersects the AFC and AVC curves at their respective minimum points.
(e) Intersects the AVC and ATC curves at their respective minimum points
Answers
Answer:
c
Explanation:
The marginal cost curve image has been attached from which we can clearly, indicate that
ATC = average total cost
AFC = average fixed cost
AVC = average variable cost.
From the graph we can indicate that the marginal cost curve
(c) Lies above the AVC curve when the AVC curve slopes downward.
Dr. Bishop wants to study how small children respond to scary stimuli. She will explain the procedure to parents and ask them to sign a permission form. She will have 3-5 year old kids individually come into her lab
Each child will be given a teddy bear to cuddle with. She will then stand a couple of feet behind the child as he or she plays and make a very loud scary sound. She will observe and measure the child's responses. The
child will come back in a few days and be given the teddy bear again, she will measure any reactions the child has to the bear.
What might an ethics review committee decide about the proposal?
The proposal is approved, as it meets the ethical guidelines defined by the APA
O The proposal is approved, because there is no deception
The proposal is denied, because participants wil ikely suffer psychological harm.
O The proposal is denied, because participants are not allowed to leave the study
The proposal is denied, because it does not meet confidentiality standards
Answers
Answer:
The correct option is;
The proposal is denied, because participants will likely suffer psychological harm
Explanation:
Among the recommendations in the report on ethical research with children, it is suggested that the following should be observed by researchers;
1) Seeking consent should be a continuous process
2) Contemplate payment forms other than money to allow more discretion on child safety
3) Have two way communication with the child
4) Ask for assent of the child participating in the research
The above APA suggestions where not met by the researcher in the study.
Answer:
The proposal is denied, because participants will likely suffer psychological harm.
Explanation:
This proposal would cause psychological harm to its participents.
I also took the test and that was the correct answer.
A machine can never be 100% efficient because some work is always lost due to which factor? friction gravity static input force
Answers
Explanation:
Hi,
The answer is friction.
There is almost no machine which are not affected by friction. It losts some work due to friction while working.
Hope it helps..
Answer:
friction
Explanation:
the other options dont effect efficiency
A car accelerates at a rate of 3 m/s^2. If its original speed is 8 m/s, how many seconds will it take the car to reach a final speed of 25 m/s?
Answers
Answer:
[tex]\Large \boxed{\mathrm{5.67 \ seconds }}[/tex]
Explanation:
[tex]\displaystyle \mathrm{acceleration \ = \ \frac{final \ velocity - initial \ velocity }{elapsed \ time}}[/tex]
[tex]\displaystyle A \ = \ \frac{V_f - V_i }{t}[/tex]
[tex]\displaystyle 3 \ = \ \frac{25 - 8 }{t}[/tex]
[tex]\displaystyle 3 \ = \ \frac{17 }{t}[/tex]
[tex]\displaystyle t \ = \ \frac{17 }{3} \approx 5.67[/tex]
an astronaut takes a tuning fork with her to the moon she strikes it inside the cabin the cabin is normally filled with air so the humans inside the spacecraft are comfortable she also strikes it outside the spacecraft when she gets down on the surface of the moon which of the following is true about the tuning fork?
A: it does not vibrate inside the spacecraft
B: id does not vibrate on moon surface
C: it vibrations are not transmitted inside the spacecraft
D:it's vibrations are not transmitted to the moon's atmosphere
Answers
Answer:
The correct option is;
D: Its vibrations are not transmitted to the moon's atmosphere
Explanation:
A tuning fork is used to produce sound by vibration such that the tune produced is pure
The tune, sound, produced by the tuning fork is transmitted as sound wave through the air by means of the gases of the air as a transmission medium so people at a distance that have air around them can hear the tuning fork sound
On the Moon's surface, the atmosphere is very and it is referred to technically as an exosphere, so the sound of the tuning fork has no medium through which to transmit and therefore, it is not transmitted on the Moon's atmosphere.
A container contains 200g of water at initial temperature of 30°C. An iron nail of mass 200g at temperature of 50°C is immersed in the water. What is the final water temperature? State the assumptions you need to make in your calculations.
[Given the value of specific heat capacity of water is 4200 J kg^-1 °C^-1 and that of iron is
450 J kg^-1 °C^-1]
Answers
Answer:
The final temperature is 31.94°
Explanation:
The mass of the water in the container m₁ = 200 g = 0.2 kg
The initial temperature of the water, T₁₁ = 30°C
The mass of the iron, m₂ = 200 g = 0.2 kg
The temperature of the iron T₂₁= 50°C is immersed in the water,
The specific heat capacity of the water, c₁ = 4200 J/(kg·°C)
The specific heat capacity of the iron, c₂ = 450 J/(kg·°C)
Heat capacity relation is given by the formula;
Heat capacity Q = Mass, m × Specific heat capacity, c × Temperature change, (T₂ - T₁)
Given that energy can neither be created nor destroyed, and with the assumption that all the heat lost by the nail is gained by the water we have;
Heat lost by iron nail = Heat gained by the water
m₁ × c₁ × (T₂ - T₁₁) = m₂ × c₂ × (T₂₁ - T₂)
Where, T₂ is the final temperature
0.2 kg × 4200 J/(kg·°C) × (T₂ - 30) = 0.2 kg × 450 J/(kg·°C) × (50° - T₂)
840·T₂ - 25200 = 4500 - 90·T₂
4500 + 25200 = 840·T₂ + 90·T₂
29700 = 930·T₂
T₂ = 29700/930 = 31.94°.
The final temperature = 31.94°.
If the s – t graph of a particle is parallel to the t – axis, the speed of the particle is (a) zero (b) constant (c) infinite (d) non-uniform
Answers
Answer:
(b) constant
Explanation:
parallel to t - axis means, at all the times, the s component does not change, it remains same, i. e., the speed is constant.
:-)
Answer:
zero
Explanation:
if the velocity time graph is parallel to the time axis its mean body has not covered the path in other words body is at rest.So the velocity of the body should be zero
so the speed is zero
hope my answer will help u
Please answer, it's really urgent A boy performs an experiment to measure the speed of sound. He stands 100 meters away form a large wall and claps his hands to make an echo. He claps again as soon as he was the echo, He does this ten times, each time clapping an soon as he hears the echo. The time between the first clap and the tenth echo a recorded. Why it better to time ten echoes together rather than just one echo?
Answers
Answer:
Explanation:
The speed of sound is very high . It is about 340 m /s . In one echo , it takes approximately
2 x 100 / 340
= .6 sec
In 10 simultaneous echo , it will take 6 s . It is difficult to measure .6 sec but to measure 6 s is easy and it can be made with greater precision , so we can calculate velocity of sound with great precision .
This is the reason why , instead of one echo , 10 echos are made and duration of 10 echo is measured , rather than making one echo and measuring time of one echo .
Open the attached image to see the question.
Answers
Answer:
option A
Explanation:
STOVE RADIATE ENERGY
A student measures the depth of a water well with an adjustable frequency audio oscillator. 2 successive resonant frequencies are heard at 40Hz and 50Hz. What is the depth of the well?
Answers
Answer:
17.15 m
Explanation:
Assuming the well is empty (full of air instead of water), the speed of sound is v = 343 m/s.
The water well acts as a pipe closed at one end. Therefore, the depth of the water well must be an odd multiple of a quarter of the resonant wavelength.
L = (2n − 1) λ/4, n = 1, 2, 3, etc.
v = λf, so λ = v/f. Substituting:
L = (2n − 1) v/(4f)
Solving for frequency:
f = (2n − 1) v/(4L)
The difference between two successive resonant frequencies is therefore:
Δf = (2(n+1) − 1) v/(4L) − (2n − 1) v/(4L)
Δf = (2n + 1) v/(4L) − (2n − 1) v/(4L)
Δf = 2 v/(4L)
Δf = v/(2L)
Plugging in values:
50 Hz − 40 Hz = 343 m/s / (2L)
2L = 34.3 m
L = 17.15 m
