the frequency of a wave in a stretched string depends on the length L, tension T and linear density m with dimension ML-1 . deduce the formula for f in terms of L , T and M using dimensional analysis​

Answers

Answer 1

Answer:

[tex]f = \frac{1 }{L}\sqrt{\frac{T}{m} }[/tex]

Explanation:

Let the frequency ,

[tex]f = L^{x}T^{y}m^{z}[/tex]

Now the unit of frequency is hertz = s⁻¹ = T⁻¹ where T is time, tension T = kgm/s² = MLT⁻¹ and linear density m = kg/m = ML⁻¹.

So,

[tex]T^{-1} = L^{x}[MLT^{-2} ]^{y}[ML^{-1} ]^{z}\\[/tex]

collecting the like bases, we have

[tex]T^{-1} = [L^{x + y -z}][M^{y + z} ][T^{-2y} ] \\L^{0} M^{0} T^{-1} = [L^{x + y -z}][M^{y + z} ][T^{-2y} ][/tex]

Equating powers on both sides, we have

x + y - z = 0  (1)

y + z = 0       (2)

-2y = -1         (3)

From (3), y = 1/2

From (2), z = -y = -1/2

Substituting y and z into (1), we have

x + y - z = 0

x + 1/2 - (-1/2) = 0

x + 1/2 + 1/2 = 0

x + 1 = 0

x = -1

So,

[tex]f = L^{x}T^{y}m^{z}\\f = L^{-1}T^{\frac{1}{2} }m^{\frac{-1}{2} }[/tex]

[tex]f = \frac{1 }{L}\sqrt{\frac{T}{m} }[/tex]


Related Questions


Which organelle is the location where mRNA is translated into a protein?

Answers

Answer:

its ribosomes. In eukaryotes, mature mRNA molecules must leave the nucleus and travel to the cytoplasm, where the ribosomes are located.

Answer:

ribosomes

Explanation:

Drag the tiles to the correct boxes to complete the pairs.
Match the mRNA sequences to their DNA sequences.

Answers

1.) UUUUUAACG
2.) CCGAAAUGU
3.) AUUACGCAU
4.) GAUCAUUAC

What's the role that oysters play in keeping the ratio of floating algae to sea floor algae levels of the bay healthy

Answers

Answer:

Oysters were keeping the nutrient levels relatively stable in the bay by filtering the nutrient sewage, animal waste, and fertilizer that was running into the bay.

Explanation:

How does an organism obtain CO2, H2O, and energy
to undergo photosynthesis?

Answers

Answer:

To perform photosynthesis, plants need three things: carbon dioxide, water, and sunlight.

Explanation:

By taking in water (H2O) through the roots, carbon dioxide (CO2) from the air, and light energy from the Sun, plants can perform photosynthesis to make glucose (sugars) and oxygen (O2).

what is combination reaction?

Answers

COMBINATION REACTION:

Combination reaction is a reaction where two or more elements or compounds combine to form a single compound. Such reactions are represented by equations of the following form: X + Y → XY. The combination of two or more elements to form one compound is called combination reaction

An example could be lithium reacting with sulfur to give lithium sulfide. When magnesium burns in air, the atoms of the metal combine with the gas oxygen to produce magnesium oxide.

Neurons that respond to specific types of lines are examples of:
A. figure detectors.
B. top-down processors.
C. feature detectors.
D. figure processors.

Answers

Answer:

C

Explanation:

Neurons that respond to certain types of lines are examples of feature detectors found in Option C. Neurons are the monomeric units of the nervous system that play an important role in transmission.

   

What is the importance of the neuron?

The neuron is a unit in which the message is transmitted from the neuron to another neuron, and this can be done by either chemical signaling or by electric signaling. The neuron receives sensory stimuli from the sensory organ and transmits them to the spinal cord.

Later, the message from the spinal cord is sent to the motor organs, and the whole pathway of the neuron signaling from the sensory to the motor organ is called the reflex arc. The neuron takes part in the signaling process so that the muscle can function, regulate the contraction relaxation, and perform many other functions.

Hence, neurons that respond to certain types of lines are examples of feature detectors found in Option C.

Learn more about the neuron here.

https://brainly.com/question/29462317

#SPJ5

If you wanted to find an ant's stomach, where would
you look?
a. Inside its head
b. Inside its cephalothorax
c. Inside its thorax
d. Inside its abdomen

Answers

Answer:

d. Inside its abdomen

Explanation:

Hope this helps!

D, inside its abdomen

anybody know how to do this?​

Answers

Answer:

Sorry

Explanation:

Sorry I don’t understand to so I can’t help you

Of the three states of matter -- solid, liquid, and gas -- which one exerts the highest pressure on its container, and why?

Answers

Answer:

gas because its going super fast and free

Explanation:

What do we call an organism that is not native to an environment, but is able to thrive anyway?

Answers

Answer:

An invasive species

Explanation:

Invasive species come from other environments, many times on accident, but usually thrive so much that they end up taking over and starving other native creatures by taking the resources. Hope this helps! (Brainliest appreciated :))


What would happen if there was too much Carbon Dioxide in the atmosphere? What if there were no processes to pull Carbon
Dioxide out of the atmosphere?

Answers

We would die because if humans take in to much Carbon Dioxide but no oxygen it would become harder to breathe CD poisoning can effect the central nervous system. The earth would turn very hot and increase the process of global warming

The Milky Way galaxy was given its name because of what it looks like when viewed from Earth.
True False

Answers

Answer:

false. we cant see the whole galaxy from earth.

Answer:

the answer is false

Explanation:

we can't see the milky way (galaxy) from earth, its impossible since its so far away. unless we used a telescope maybe, not sure but for this question its false. I hope this helped!

☁️☁️☁️☁️☁️☁️☁️

What macromolecules would you find in Blazin' wings and celery?​

Answers

Carbohydrates, proteins and lipids.

What happens during the pathway of glycolysis?

A. Glucose is broken down into private

B. Carbon dioxide is produced

C. More ATP is consumed than is produced.

D. Lactic acid is produced

Answers

Answer:

the correct answer is A :Glucose is broken down into pyruvate

Answer:

If I'm correct, the glucose is broken down into pyruvate and energy.

Explanation:

I hope this helps! ^^

☁️☁️☁️☁️☁️☁️☁️

HELP ASAP PLS IF U ANSWER U GET 40 POINTS THANKS

Answers

Explanation:

The grass help feeds the baboon. This means the baboon will have to poop out the grass. Then the dung bettle feeds off of that poop.

Which amino acids are coded for from the DNA sequence TACCAGCCA?
methionine, valine, and glycine


methionine, glutamine, and alanine


methionine, valine, and aspartic acid


arginine, histidine, and cysteine
Where do the instructions for building a protein originally come from?
tRNA


rRNA


DNA


mRNA
A _______________ is composed of a series of amino acids.
Molecule


Protein


Nucleotide


Cell

Answers

Explanation:

DNA

The instructions for building a protein originally come from DNA, which is the store for all hereditary information.

A protein is composed of a series of amino acid.

Brady took a cutting from a sweet potato vine in his family garden and placed the vine in a small vase filled with water. After about a week, tiny roots had begun to grow. What is this an example of

Answers

Answer:This is an example of asexual reproduction.

Explanation:

Reproduction is defined as the ability of living organisms to produce offspring, that is, new individuals of their type. Living organisms have developed many methods of reproducing. These can be either ASEXUAL or SEXUAL.

Asexual reproduction: In asexual reproduction, an individual produces an offspring by itself, that is, only one parent is present. This type of reproduction is common among flowering plants. Examples of asexual reproduction includes:

--> Fission

--> Budding

--> Spore formation

--> Fragmentation and

--> Vegetative propagation.

The sweet potato vine is reproduced by an asexual means known as vegetative propagation. Here, a new plant grows from any portion of an old one other than the seeds. When stem cutting are taken from the vine, new storage roots are formed within few days.

Brady took a cutting from a sweet potato vine in his family garden and placed the vine in a small vase filled with water. After about a week, tiny roots had begun to grow which is an example of - Asexual reproduction.

Asexual reproductionis a type of reproduction that does not involve the fusion of gametes or change in the number of chromosomes.Examples of asexual reproduction include:   Fission  Budding  Spore formation  Fragmentation and  Vegetative propagation.In the given scenario sweet potato is cultivated by vegetative propagation.Brady takes stem cuttings from the vines, which then root and form new storage roots.Sweet potatoes are relatively easy to propagate by rooting vine cuttings directly in the ground or in a well-drained rooting media

Thus, The given case shows an example of - asexual reproductions.

Learn more:

https://brainly.com/question/13876478

Choose which statement best describes an element.

A. Anything that takes up space

B. A pure substance that cannot be broken down into other substances by chemical means.

C. Water

D. Atom has a nucleus with neutrons and protons in it.​

Answers

Answer:

B

Explanation:

Elements are pure substances that cannot be broken down into other substances by chemical means .

Suppose the phloem of a seed plant is damaged and does not function properly.
How will this most directly affect the plant?

Answers

Answer:

Food will not be carried away from the leaves

Explanation:

1. How many kinds of nitrogen bases does a DNA molecule have?
A. 2
B. 3
C. 4.
D. 1

Answers

Answer:

4.

Explanation:

Adenine, Thymine, Cytosine, and Guanine

(In RNA Thymine is replaced with Uracil)

If a strand of DNA has the nitrogen base sequence, GCTAGATGCG, what will be
the sequence of the complementary strand?

Answers

Answer:

CGATCTACGC

Explanation:

The complementary strand of DNA to GCTAGATGCG is CGATCTAGCT.

The nitrogen bases in DNA are complementary to each other. This means that adenine (A) always pairs with thymine (T), and guanine (G) always pairs with cytosine (C).

The strand of DNA GCTAGATGCG has the following sequence of nitrogen bases:

G - guanineC - cytosineT - thymineA - adenineG - guanineA - adenineC - cytosineG - guanine

The complementary strand of DNA will have the following sequence of nitrogen bases:

C - cytosineG - guanineA - adenineT - thymineC - cytosineT - thymineG - guanineC - cytosine

The complementary strand is created by pairing the nitrogen bases in the original strand with their complementary bases. So, the guanine in the original strand pairs with the cytosine in the complementary strand, the cytosine in the original strand pairs with the guanine in the complementary strand, and so on.

To know more about the Sequence, here

https://brainly.com/question/29457800

#SPJ2

Please help only 2 questions, multiple choice

Answers

The first answer is homeostasis so d

The second answer is organelle so c

7. Which of the following is not an example of an abiotic factor?
O Water
O Soil
O Disease
O Air
Please help

Answers

Answer:

Disease

Explanation:

Water, Soil and Air are all biotic except for disease.

Yes that’s right absolutely

How can you determine the number of bonds an atom can make

Answers

Answer:

The number of bonds for a neutral atom is equal to the number of electrons in the full valence shell (2 or 8 electrons) minus the number of valence electrons. This method works because each covalent bond that an atom forms adds another electron to an atoms valence shell without changing its charge.

Match each gymnosperm to its correct description. plzzz help me reeee​

Answers

Answer:

Explanation:

Ginkgoes lose their leaves in autumn

Cycads look like a palm tree

Gnetophytes grow in deserts and rain forests

Conifers make up the largest group of gymnosperms.

Each gymnosperm is matched according to their correct description

Ginkgoes lose their leaves in autumnCycads look like a palm treeGnetophytes grow in deserts and rain forestsConifers make up the largest group of gymnosperms.

What are Gymnosperms?

Gymnosperm is a seed-producing plant which do not produce flowers or fruits and have uncovered seeds. These are born in cones and are not visible until maturity.

There are several characteristics of Gymnosperms. They are:

1. They are autotrophic, photosynthetic plants which tend to conserve water.

2. They have vascular system which includes roots, xylem, and phloem that is used for the transportation of water and nutrients.

3. The ovules and seeds of gymnosperms develop on the scales of cones which is in enclosed chambers called ovaries.

4. They are older than angiosperms on the basis of evolution.

They are divided into four classes like

Ginkgoes Cycads Gnetophytes Conifers

Thus, each gymnosperm is matched according to their correct description

Ginkgoes lose their leaves in autumnCycads look like a palm treeGnetophytes grow in deserts and rain forestsConifers make up the largest group of gymnosperms.

Learn more about Gymnosperms, here:

https://brainly.com/question/17194627

#SPJ2

what are the pros and cons of online school​

Answers

Answer:

The Pros and Cons of Studying Online

Pro: Increased Flexibility. The biggest advantage to studying online is the increase in flexibility. ...

Con: Reputation. Many firms and institutions are quick to dismiss an online education. ...

Pro: Ease of Access. ...

Con: Lack of Social Interaction. ...

Pro: More Affordable. ...

Con: Fewer Courses.

Pros of Online Schools:

Time flexibility.

Availability.

24/7 access to course material..

Location flexibility.

Zero commute.

Self-Direction.

Multi-media presentations.

Variety of course options.

Cons of Online Schools:

Limited interaction with instructor.

Technology requirements.

Social interaction.

Campus environment.

Time management.

Stigma.

Credit transfer.

Financial aid.

Have a wonderful day!

Which geological feature would most likely occur at this boundary? (the plates are the same density.)

A) mid-ocean ridge, rift vallyes
B) earthquakes
C) volcanos
D) mountain chains

Answers

A

mid ocean ridges occur along divergent plate boundaries

Answer:

a

Explanation:

The relationship that occurs between an orchid attached on a narra tree could be
classified as Commensalism and Parasitism. True or false?

Answers

Answer:

Yes, it's True

Explanation:

A parasitic relationship helps one of the species involved in the relationship, but harms the other organism in the process of it growing. It is a symbiotic relationship and would be classified as Commensalism. Most of the orchids are epiphytes, so they tend to grow on other plants. hope you understand. Fighting!

The relationship that occurs between an orchid attached on a narra tree could be classified as Commensalism. Thus, the given statement is true.

What is Commensalism?

Commensalism is a long-term biological interaction or symbiosis in which the members of one species gain benefits which help them in survival while those of the other species are neither benefitted nor are harmed from the association.

In contrast with mutualism, in which both the organisms benefit from each other and amensalism, where one species is harmed while the other species is unaffected and that of parasitism, where one species is harmed and the other species benefitted.

Learn more about Commensalism here:

https://brainly.com/question/14224704


#SPJ2

All multicellular algae are what?

Answers

Answer:

Algae (singular: alga) are photosynthetic, eukaryotic organisms that do not develop multicellular sex organs. Algae can be unicellular, or they may be large, multicellular organisms.The multicellular algae develop specialized tissues, but they lack the true stems, leaves, or roots of the more complex, higher plants.

Explanation:

Does mass alone determine whether an object will float or sink? Explain

Answers

Answer:

yes because if the mass is heavy it gonna sink, if its light its gonna float

Explanation:

Other Questions
Where does buck fall among the hierarchy? One scientist suggests that out of the different possible locations, they should design the model and build it at the equator recieves the most intense solar radiation. Which if the following is the most appropriate critique for the scientist's suggestion?A. Earth's equator is not hot enough to simulate the Martian daytime.B. The high mountain top gets the same amount of radiation as the equator, but with atmospheric conditions that are more similar to Mars.C. The equator has deserts that are actually too dry compared to Mars. D. The Antarctica has the same nighttime temperature as Mars, but with a similar amount of ice compared to the equator. help please i give the best one brainlyest 14. A right cone has a height of 14 in and a base diameter of 17 in.a Sketch and label a diagram of the coneb. Determine the area of the lateral surface of the cone, to the nearest square inch The management of Ballard MicroBrew is considering the purchase of an automated bottling machine for $61,000. The machine would replace an old piece of equipment that costs $15,000 per year to operate. The new machine would cost $6,000 per year to operate. The old machine currently in use could be sold now for a salvage value of $20,000. The new machine would have a useful life of 10 years with no salvage value. Required: 1. What is the annual depreciation expense associated with the new bottling machine urgent help! right now everyone any one a single pringle and need a hug Can someone please help me ASAP hey guys! im doing the g-o-o-g-l-e doodle contest and i want some ideas for what i should do the theme is, "i am strong because..." and make sure it's kid friendly (ur ideas) Use the Proportionality Theorem to solve for X. Pls help im an idiot and cant solve this first gets brainliest Online, it is easy to think of communication as computer to ____________ rather than _________ to ___________.a.person, computer, personb.computer, person, computerc.person, person, persond.computer, person, person Edge-law enforcementFor which reason do corrections facilities pursue accreditation? (Select all that apply.)-to protect themselves from lawsuits-to comply with the law-to comply with national standards-to demonstrate to the public that the facility is operating under rule of law (310^3 )(410^6)=??? What is the formula for the following arithmetic sequence?-9, -2, 5, 12, ...an = -9 + 7( n - 1)an = -9 + (-7)( n - 1)an = 7 + (-9)( n - 1)an = 9 + (-7)( n - 1) This is for anatomy, please help asap! :) Thank you! a tree is broken at a height of 6 cm from the ground and its top touches the ground at a distance of 8cm from the base of the tree . find the original height of the tree pls do to step to step explaination What is gross domestic product check all that apply.A.is it the total profit that all the corporations in an economy make in one yearB.Its the total amount of money that consumers in an economy have to spendC.Its the total amount of goods and services that a nation produces within a yearD.its the total expenses used to produce all the goods and services in a nation 234.2 in expanded form Simplify3x- 2z+- 2z- 4z- 3z