Wavelength Formula

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Wavelength Formula

Wavelength is the distance between the crests of a wave. Many different things can move like waves, like strings, water, the air (sound waves), the ground (earthquakes), and light can be treated as a wave. Wavelength is represented with the Greek letter lambda: λ. It is equal to the velocity of the wave, divided by the frequency. Wavelength is expressed in units of meters (m).

λ = wavelength, the distance between wave crests (m)

v = wave velocity, the speed that waves are moving in a direction (m/s)

f = frequency, the wave crests that go through a point in a certain time (cycles/s or Hz)

Wavelength Formula Questions:

1) The speed of sound is about 340 m/s. Find the wavelength of a sound wave that has a frequency of 20.0 cycles per second (the low end of human hearing).

Answer: The wave velocity v = 340 m/s, and the frequency f = 20.0 cycles/s. The wavelength ? can be found using the equation:

λ = 17.0 m

The wavelength of the sound is 17 meters.2) A motor boat makes waves that travel across the surface of a lake. The waves travel toward shore at a velocity of 1.50 m/s. The distance between wave crests is 2.00 m. What is the frequency of the waves?

Answer:: The wave velocity v = 1.50 m/s, and the wavelength λ = 2.00 m. The frequency must be solved for, so rearrange the equation:

f = 0.75 waves/s

The frequency of these water waves is 0.75 waves per second.

Velocity Formula

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Velocity is a measure of how quickly an object moves. So, the velocity is the change in the position of an object, divided by the time. Velocity has a magnitude (a value) and a direction. The unit for velocity is meters per second (m/s).

v = velocity (m/s)

xf = the final position (m)

xi = the initial position (m)

t = the time in which the change occurs (s)

Δx = short form for “the change in” position (m)

Velocity Formula Questions:

1) A sail boat is in a 1000 m race, and it crosses the starting line when it is already at full speed. It reaches the finish line in exactly 1 minute and 20 seconds ( = 80.0 s). What is the velocity of the sail boat?

Answer: The initial position is the starting line, which we can give the value xi = 0.00 m. The finish line is 1000 m from the start, so xf = 1000 m. The time it takes the sail boat to travel that distance is t = 80.0 s. The velocity can be found using the equation:

v = 12.5 m/s

The velocity is 12.5 m/s, in the direction of the finish line.

2) Each floor in a tall building is 3.00 m high. When it’s moving, the elevator in this building moves at a constant velocity of 1.50 m/s. If the first floor is at position 0.00 m, the second floor is at position 3.00 m, and so on, how much time does it take for the elevator to go from the sixth (6th) to the eighteenth (18th) floor?

Answer: The initial and final positions of the elevator can be found using the floor numbers and the distance between floors. The initial floor is 6, so the initial position is:

xi = (6)(3.00 m)

xi = 18.0 m

and the final floor is 18, so the final position is:

xf = (18)(3.00 m)

xf = 54.0 m

The velocity (which we assume to be constant) is v = 1.50 m/s. The time must be found, so rearrange the equation:

t = 24.0 s

The time it takes for the elevator to travel from the sixth to the eighteenth floor is 24.0seconds.

Frequency Formula

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Frequency is the number of cycles in a unit of time. The “cycles” can be movements of anything with periodic motion, like a spring, a pendulum, something spinning, or a wave. Frequency is equal to 1 divided by the period, which is the time required for one cycle.

The derived SI unit for frequency is hertz, named after Heinrich Rudolf Hertz (symbol hz). One hz is one cycle per second.

f = frequency, the cycles in a unit of time

T = period, the time required for one cycle

N = a number of cycles

t = an amount of time

Frequency Formula Questions:

1) A long pendulum takes 5.00 s to complete one back-and-forth cycle. What is the frequency of the pendulum’s motion?

Answer: The pendulum takes 5.00 s to complete one cycle, so this is its period, T. The frequency can be found using the equation:

f = 0.20 cycles/s

The frequency of the pendulum is 0.20 cycles/s. The units cycles/s are often written as “Hertz”, with the symbol “Hz”. So, the frequency of this pendulum can also be stated as 0.20 Hz.

2) The tachometer in a car measures the revolutions per minute of the tires (revolutions and cycles are the same thing). A car is travelling at a constant speed, and the tachometer reads 2400 revolutions per minute. What is the frequency of the tires spinning, measured in cycles per second? What is the period, in seconds?

Answer: The number of cycles (revolutions) to consider is 2400. This is the number of cycles that happen in one minute, which is equal to 60 seconds. So, the frequency can be found using the equation:

f = 40 cycles/s

The frequency of the tires spinning is 40 cycles/s, which can also be written as 40 Hz. To find the period from this, rearrange the equation that relates period and frequency:

T = 0.025 s

The period of the tires spinning is 0.025 seconds.

UC BERKELEY’S LUSEE SELECTED FOR 2021 MOON LANDING

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Tuesday, July 2, 2019 / Physics at Berkeley News

Scavenging spare parts and grabbing off-the-shelf hardware, University of California, Berkeley, space scientists are in a sprint to build scientific instruments that will land on the moon in a mere two years.

NASA announced yesterday that it has selected 12 scientific payloads to fly aboard three lunar landing missions within the next few years. One of them will be the Lunar Surface Electromagnetics Experiment (LuSEE), which will be built under the direction of Stuart Bale, a UC Berkeley professor of physics and a veteran of several past NASA missions, including the Parker Solar Probe that was launched last August.

The science and technology experiments will explore the moon’s surface environment in advance of upcoming human missions and are part of NASA’s collaboration with commercial partners to launch payloads — and, by 2024, humans — to the moon.

Bale and his colleagues at UC Berkeley’s Space Sciences Laboratory have less than $6 million to cover the costs, which means they will be co-opting spare parts originally built for the Parker Solar Probe and other spacecraft, including STEREO, which launched in 2006 and is still providing stereo views of the sun, and the 2013 MAVEN on a mission to Mars. The LuSEE will make comprehensive measurements of electromagnetic phenomena on the surface of the moon and erect a simple radio telescope — the first operational telescope on the moon.

“NASA wanted instruments that are ready to go, because the schedule is really aggressive. We are talking about pulling something together and delivering it in about 18 months, which is fast,” Bale said. “We proposed a re-flight of our Parker Solar Probe instrumentation, which works like a charm, and the team is still together to get it tuned up. We’re good at building experiments quickly and that work.”

“Berkeley is going to put an experiment on the surface of the moon,” Bale added. “That is pretty cool, I think.”

Two-week lifespan?
The experiment is not expected to last longer than one lunar day — about two weeks — because the batteries will discharge during the two weeks of night. But Bale is hoping it will survive the lunar darkness and live to observe another lunar day.

“The thermal environment is really nasty on the dark side, so we will land at morning, when the sun comes up on the moon, spend two weeks — one lunar daylight — observing like crazy, and when it becomes night, the lander goes into the dark and the batteries will run down because there is no solar input to recharge them. They are not required to wake up on the other side.”

The missions are part of NASA’s Commercial Lunar Payload Services program, which on May 31 commissioned three upstart companies to build lunar landers to return NASA to the moon 50 years after America last landed a spacecraft there: the Apollo 17 manned mission in 1972. These landers will carry the 12 payloads, seven of which will focus on answering questions in planetary science and heliophysics, and five on demonstrating new technologies.

“These new lunar payloads represent cutting-edge innovations that will help us get to know the moon as we never have before, as we prepare to land humans on the moon and, eventually, Mars,” said Thomas Zurbuchen, associate administrator of the agency’s science mission directorate in Washington, D.C. “Each one brings something new to the moon and can take advantage of early flights through our commercial partnership program.”

One of the three landers will carry LuSEE, which will measure the moon’s fluctuating magnetic field and the dust kicked up by light and electrons coming from the sun.

Dust could be a big problem for future moon colonists, Bale said. Harrison Schmitt, who crewed Apollo 17, suffered an allergic reaction to moon dust, as did a doctor who unloaded Schmitt’s spacesuit upon return to Earth. The fine dust was also a nuisance inside the Apollo landers, because it is electrically charged and sticks to everything.

The moon’s surface is electrostatically charged, too, which could cause problems for structures and humans on the moon. Apollo astronauts saw fountains of dust thrown into the air at the day-night boundary of the moon, presumably because of voltage differences between the lit and unlit portions of the moon. The voltage differences can also charge up objects on the surface, leading to sparking.

Bale is interested in how the electrostatic environment on the surface changes as the sun moves across the sky and how that changing electrostatic environment affects the dust. Magnetometers on board will measure changes in the magnetic field, which have to date only been measured indirectly by spacecraft orbiting the moon, using instruments built at the Space Sciences Laboratory.

The LuSEE will also carry the first U.S. radio telescope on the moon, a simple dipole antenna that is like a rabbit-ear TV antenna. The antenna will be identical to the one aboard the Parker Solar Probe, which so far has been able to record radio emissions from the Milky Way Galaxy in frequency ranges not possible to detect on Earth, because such wavelengths are blocked by ions in the atmosphere.

“I am sure we will see the sun — solar flares, type 3 radio storms, coronal mass ejections — but also Jupiter and other planets, which we already see with the solar probe,” Bale said. “And we will see a lot of emissions from Earth. We propose to do a survey of the radio environment on the surface of the moon in preparation, someday, for a more advanced radio telescope.”

Such a solar array on the moon could answer questions about the early history of the universe, including the “epoch of reionization,” when the first stars began to form in the universe, about 400 million years after the Big Bang.

Source: Berkeley News

Editor: Robert SandersResearch

Area: Astrophysics

Frequency Formula

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Frequency is the number of cycles in a unit of time. The “cycles” can be movements of anything with periodic motion, like a spring, a pendulum, something spinning, or a wave. Frequency is equal to 1 divided by the period, which is the time required for one cycle.

The derived SI unit for frequency is hertz, named after Heinrich Rudolf Hertz (symbol hz). One hz is one cycle per second.

f = frequency, the cycles in a unit of time

T = period, the time required for one cycle

N = a number of cycles

t = an amount of time

Frequency Formula Questions:

1) A long pendulum takes 5.00 s to complete one back-and-forth cycle. What is the frequency of the pendulum’s motion?

Answer: The pendulum takes 5.00 s to complete one cycle, so this is its period, T. The frequency can be found using the equation:

f = 0.20 cycles/s

The frequency of the pendulum is 0.20 cycles/s. The units cycles/s are often written as “Hertz”, with the symbol “Hz”. So, the frequency of this pendulum can also be stated as 0.20 Hz.

2) The tachometer in a car measures the revolutions per minute of the tires (revolutions and cycles are the same thing). A car is travelling at a constant speed, and the tachometer reads 2400 revolutions per minute. What is the frequency of the tires spinning, measured in cycles per second? What is the period, in seconds?

Answer: The number of cycles (revolutions) to consider is 2400. This is the number of cycles that happen in one minute, which is equal to 60 seconds. So, the frequency can be found using the equation:

f = 40 cycles/s

The frequency of the tires spinning is 40 cycles/s, which can also be written as 40 Hz. To find the period from this, rearrange the equation that relates period and frequency:

T = 0.025 s

The period of the tires spinning is 0.025 seconds.

Force Formula

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Force is the mass of an object, multiplied by its acceleration. The unit of force is . This is called a Newton, with the symbol N. Force has a magnitude and a direction.

force = mass x acceleration

F = ma

F = force

m = mass

a = acceleration

Force Formula Questions:

1) A 0.15 kg coconut falls out of its tree. The acceleration due to gravity is 9.80 m/s2, down. What is the force acting on the coconut due to gravity?

Answer: The force can be found using the equation:

F = ma

F = (0.15 kg)(9.80 m/s2)

F = 1.47

F = 1.47 N

The force due to gravity acting on the coconut is 1.47 N, down.

2) A man pushes a 50.0 kg block of ice across a frozen pond. He applies a force of 25.0 N, pushing the block away from him. What is the acceleration of the block?

Answer: To find the acceleration, rearrange the equation:

The block is accelerating 0.50 m/s2, directed away from the man.

Acceleration Formula

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Acceleration is a measure of how quickly the velocity of an object changes. So, the acceleration is the change in the velocity, divided by the time. Acceleration has a magnitude (a value) and a direction. The direction of the acceleration does not have to be the same as the direction of the velocity. The units for acceleration are meters per second squared (m/s2).

a = acceleration (m/s2)

vf = the final velocity (m/s)

vi = the initial velocity (m/s)

t = the time in which the change occurs (s)

Δv = short form for “the change in” velocity (m/s)Acceleration Formula Questions:

1) A sports car is travelling at a constant velocity v = 5.00 m/s. The driver steps on the gas, and the car accelerates forward. After 10.0 seconds, the driver stops accelerating and maintains a constant velocity v = 25.0 m/s. What was the car’s acceleration?

Answer: The initial velocity is vi = 5.00 m/s, in the forward direction. The final velocity is vf = 25.0 m/s in the forward direction. The time in which this change occurred is 10.0 s. The acceleration is in the forward direction, with a value:

The car’s acceleration is 2.00 m/s2, forward.

2) A child drops a rock off of a cliff. The rock falls for 15.0 s before hitting the ground. The acceleration due to gravity is g = 9.80 m/s2. What was the velocity of the rock the instant before it hit the ground?

Answer: The rock was released from rest, so the initial velocity is vi = 0.00 m/s. The time in which the change occurred is 15.0 s. The acceleration is 9.80 m/s2. The final velocity must be found, so rearrange the equation:

vf = vi + at

vf = 0.00 m/s +(9.80 m/s2)(15.0 s)

vf = 147 m/s

The rock is falling, so the direction of the velocity is down.