using dimensional analysis find the relation between the velocities of transverse waves produced from the vibration of thin homogeneous string and between the tension in the string and mass per unit length of it.​

Answers

Answer 1

Answer:

[tex]v^2=\frac{T}{M}[/tex]

where v = transverse wave velocity, T = tension in the string, M = mass per unit length.

Explanation:

Dimensional analysis is where you just look at the units and see how they fit within each other.

In this case, all relationships are made using the MLT comparisons, where M stands for Mass, L stands for Length, and T stands for time.

For example, for velocity, we know the SI unit for velocity is [ms⁻¹] which is L¹T⁻¹, we can do the same thing for tension = [N = Kgms⁻²] = M¹L¹S⁻², and for the mass per unit length which we can think of as [Kgm⁻¹] = M¹L⁻¹.

If you play around a little with the powers, you can find a relationship:

[tex]v^2=\frac{T}{M}[/tex]

since:

[L¹T⁻¹]² = L²T⁻² = M¹L¹T⁻² ÷ M¹L⁻¹ = M¹⁻¹L¹⁻⁽⁻¹⁾T⁻² = M⁰L²T⁻² = L²T⁻²


Related Questions

An RLC circuit is used in a radio to tune into the radio lagos fm Station broadcasting at 93.5Hz. The resistance is 15ohms and the inductance is 1.6 H. Calculate the capacitance used​

Answers

The characteristics of the RLC circuit allow to find the result for the capacitance at a resonance of 93.5 Hz is:

Capacitance is C = 1.8 10⁻⁶ F

A series RLC circuit reaches the maximum signal for a specific frequency, called the resonance frequency, this value depends on the impedance of the circuit.

            [tex]Z^2 = R^2 + ( wL - \frac{1}{wC} )^2[/tex]  

Where Z is the impedance of the circuit, R the resistance, L the inductance, C the capacitance and w the angular velocity. The negative sign is due to the fact that the current in the capacitor and the inductor are out of phase.

In the case of resonance, the impedance term completes the circuit as a resistive system.

           [tex]wL - \frac{1}{wC} = 0 \\w^2 = \frac{1}{LC}[/tex]  

           

Indicate that the inductance L = 1.6 H and the frequency f = 93.5 Hz.

Angular velocity and frequency are related.

         

         w = 2π f

           

Let's  substitute.

          [tex]C = \frac{1}{L ( 2 \pi f)^2 }[/tex]  

 

Let's calculate.

         [tex]C = \frac{1}{1.6 \ ( 2\pi \ 93.5)^2}[/tex]  

         C = 1.8 10⁻⁶ F

In conclusion with the characteristics of the RLC circuits we can find the result for the capacitance at a 93.5 Hz resonance is:

Capacitance is C = 1.8 10⁻⁶ F

Learn more about serial RLC circuits here: brainly.com/question/15595203

A rocket has a mass of 600 kg. a What is its weight on Earth where g = 10 N/kg? b At lift-off the rocket engine exerts an upward force of 26 000 N. What is the resultant force on the rocket? What is its initial acceleration?

Answers

Answer:

a) 5000

b) 40m/s this is the right answers

Explanation:

but no so so sure


The spring constant of Spring A is twice as great as the spring constant of Spring B. Both springs are stretched the same amount. How does the
force the Spring A applies compare to the force Spring B applies?

Answers

Answer:

FA = 2FB

Force on spring A is twice the Force on spring B

Explanation:

F = kx

FB = (kB)x

FA = (kA)x

FA= (2kB)x

FA = 2(kB)x

FA = 2FB

The force [tex]F_A[/tex] needed to stretch spring A is going to be twice as much as the force [tex]F_B[/tex] needed to stretch spring B.

Explanation:

We know that the spring constants are related as

[tex]k_A = 2k_B[/tex]

The force [tex]F_A[/tex] needed to stretch spring A is given by

[tex]F_A = -k_Ax[/tex]

Also, the force [tex]F_B[/tex] needed to stretch spring is

[tex]F_B = -k_Bx[/tex]

Taking the ratio of the forces, we get

[tex]\dfrac{F_A}{F_B} = \dfrac{-k_Ax}{-k_Bx} = \dfrac{k_A}{k_B}[/tex]

Since [tex]k_A = 2k_B,[/tex] the equation above becomes

[tex]\dfrac{F_A}{F_B} = \dfrac{2k_B}{k_B} = 2[/tex]

or

[tex]F_A = 2F_B[/tex]

This shows that since the spring constant of spring A is twice as large as that of spring B, the force needed is going to be twice as large.

If a wave is traveling at a constant speed, and the frequency decreases, what would happen to the wavelength?

A. It would increase.

B. It would decrease.

C. It would remain constant.

D. It would drop to zero.

Answers

It would decrease because the frequency is decreasing

Specific heat capacity
of a solid

Answers

specific heat of a solid or liquid is the amount of heat that raises the temperature of a unit mass of the solid through 1° C. We symbolise it as C. In S.I unit, it is the amount of heat that raises the temperature of 1 kg of solid or liquid through 1K

An object in free fall has a velocity of 5m/s in the upward direction. What is the instantaneous velocity of the object one second later?

Answers

Answer:

Explanation:

Near the earth's surface where gravity is approximately 10 m/s² downward

v = u + at

v = 5 + (-10)(1) = -5 m/s

so it has the same speed but in the opposite (downward) direction.

The instantaneous velocity of the object is -4.8 m/s and is directed downwards.

What is meant by instantaneous velocity ?

Instantaneous velocity is defined as the rate of change of position for a given interval of time. And it also represents the direction.

Here,

The object is freely falling.

So, the acceleration of the object is the acceleration due to gravity.

a = g = 9.8 m/s²

Initial velocity of the object, u = 5 m/s  (upward velocity)

Time given, t = 1

Using the first equation of motion,

v = u + at

v = 5 + (-9.8) x 1  

( negative sign is due to it is directed downwards which is opposite to u)

v = -4.8 m/s

That means the instantaneous velocity is directed downwards.

Hence,

The instantaneous velocity of the object is -4.8 m/s and is directed downwards.

To learn more about instantaneous velocity, click:

https://brainly.com/question/2273637

#SPJ3

A train travels at 40m/s. Calculate the time it takes to travel:
A) 30,000 m
B) 50 km

Answers

Answer:

a is 750 second

b is 2 hour

The time it takes for the train to travel 30,000m and 50,000m is 750seconds and 1250 seconds, respectively.

What is speed?

The speed is the distance covered by an object at a particular time. Therefore, it is the ratio of distance and time.

[tex]\rm{Speed = \dfrac{Distance}{Time}[/tex]

A train travels at 40m/s. Now, the time it takes to travel the given distance is,

A.) 30,000m

Speed = Distance / Time

Time = Distance / Speed

Time = 30,000m / 40m/s

Time = 750 seconds

B.) 50 km

1 km = 1000m

50 km = 50 × 1000m = 50,000 m

Speed = Distance / Time

Time = Distance / Speed

Time = 50,000m / 40m/s

Time = 1250 seconds

Hence, the time it takes for the train to travel 30,000m and 50,000m is 750seconds and 1250 seconds, respectively.

Learn more about Speed here:

https://brainly.com/question/15100898

#SPJ2

A 3.1 kg ball is dropped from the top of a 38 m tall building. What is the speed of the ball when it is halfway from the building to the ground? Round your answer to 2 decimal places.

Answers

Answer:

19.3m/s

Explanation:

Use third equation of motion

[tex]v^2-u^2=2gh[/tex]

where v is the velocity at halfway, u is the initial velocity, g is gravity (9.81m/s^2) and h is the height at which you'd want to find the velocity

insert values to get answer

[tex]v^2-0^2=2(9.81m/s^2)(38/2)\\v^2=9.81m/s^2 *38\\v^2=372.78\\v=\sqrt[]{372.78} \\v=19.3m/s[/tex]

what forces would a person inside an elevator feel when it is going up?

Answers

Hey there.

So there are a few forces that act upon a person in an elevator. The first is Gravity. This is the downward force keeping us on the floor of the elevator. The second, is the upward force from where the cable takes the elevator upwards. The tension which is present means that for a short period of time, we are pushed into the floor more and our mass goes up.

Hope this helps :)

A runner of mass 80 kg is moving at 8.0 m/s. Calculate her kinetic energy. ​

Answers

Answer:

2560J

Explanation:

By definition the kinetic energy can be calculated in the following way:

K = (mv²)/2 = 80kg·(8.0m/s)²/2 = 2560 J

Two moles of an ideal monatomic gas go through the cycle abc. For the complete cycle, 800 J of heat flows out of the gas. Process ab is at constant pressure, and process bc is at constant volume. States a and b have temperatures Ta = 200 K and Tb = 300 K.
(a) Sketch the all possible pV-diagrarns for the cycle.
(b) What is the work W for the process ca?

Answers

a) Sketches of all possible pv-diagrams for the cycle are attached below

b) The work W[tex]_{ac}[/tex] for the process Ca is : 2462.8  J

Given data :

Amount of heat flowing out = 800 J

Ta = 200 K

Tb = 300 K

R = 800

B) Determine the work W for the process Ca

Wₐs = -pdv

       = - [ pVb - pVa ] ---- ( 1 )

note : pVb = nRTb ,  pVa = nRTa

Equation ( 1 ) becomes

= -nR [ Tb - Ta ]

= - 2(8.314 ) [ 300 - 200 ]

= - 1662.87

given that W[tex]_{bs}[/tex] = 0 which is isochonic

dv = 0 ( cyclic process ) = d∅ - dw

∴ 0 = 800 - ( Wₐs  +  W[tex]_{ac}[/tex] )

Therefore : W[tex]_{ac}[/tex] = 800 + 1662.8 = 2462.8  J

Hence we can conclude that the work W for the process Ca = 2462.8  J

Learn more about Pv diagrams : https://brainly.com/question/25401637

23 A 2-kg rock is moving at a speed 6 m/s, What constant force is needed to stop the rock in 7x10-52

Answers

Answer:

Explanation:

Do you mean 7 x 10⁻⁵² seconds? Who can even measure that small a time period?

If that time is incorrect, just redo the math with the correct time to get the force.

An impulse will cause a change of momentum

FΔt = mΔv

F = mΔv/Δt

F = 2(0 - 6)) / (7 x 10⁻⁵² - 0)

F = - 1.7 x 10⁵² N

The magnitude of that force would pretty much crush any rock it hit.

stuck with this one. ​

Answers

Y is the right answer :)

A metal bar has a volume of 32 cm3. The mass of the bar is 256 g. What is the density of the metal? A. 290 g/cm3 6 B. 8,200 g/cm C. 8.0 g/cm3 O D. 220 g/cm​

Answers

The density of the metal is ρ = 8.0g/cm³.

Why is density important?

The measure of material how densely it is packed together is called density. As the mass per unit volume, it has that definition. Symbol for density: D or Formula for Density: When is the density, m is the object's mass, and V is its volume, the equation is: = m/V.

Because it enables us to predict which compounds will float and which will sink in a liquid, density is a crucial notion. As long as an object's density is lower than the liquid's density, it will often float.

Equation :

To the given equation we have :

mass of the bar = 256g

volume of metal bar = 32cm³

So according to the formula of density

ρ = m/V

So, putting values

ρ = 256g /32cm³

ρ = 8.0g/cm³

To know more about volume :

https://brainly.com/question/28058531

#SPJ1

Two satellites are in orbit around a planet. Satellite 1 has a mass of mm and an orbital radius of 2r2r. Satellite has a mass of 2m2m and an orbital radius of rr. If the magnitude of the gravitational force the planet exerts on Satellite 1 is FF, the magnitude of the gravitational force the planet exerts on Satellite 2 is
a) F
b) 1/2F
c) 2F
d) 1/4F

Answers

The magnitude of the gravitational force the planet exerts on Satellite 2 is  1/2F.

We recall that from Newton's law of universal gravitation, the gravitational force is given by;

F =G m1m2/r^2

m1 and m2 are the respective masses

r is the distance of separation.

Let the mass of the planet be M and the mass of the satellite be m. The distance of separation is r.

For satellite 1;

F = GmM/(2r)^2

F = GmM/4r^2

For satellite 2;

F2= G2mM/r^2

Hence, the magnitude of the gravitational force the planet exerts on Satellite 2 is  1/2F.

Learn more about gravitational force: https://brainly.com/question/24783651

Why is visual constancy important?

A.
It gives people the ability to see things both close up and far away.

B.
It lets people of all ages see the edges of cliffs so they don’t fall over.

C.
It allows perceptions to remain the same even as images change.

D.
It offers the chance to use one retina at a time to interpret an image.

Reset

Answers

Answer:

C.

Explanation:

Visual constancy is a key mechanism that allows the perception to remain.the same even as images change

#CARRYONLEARNING

Visual constancy is  important because it allows perceptions to remain the same even as images change.

What is  Constancy phenomenon?

Constancy phenomenon describes how people and animals tend to perceive familiar objects as having a constant shape, size, colour, or location regardless of adjustments to distance, illumination, or perspective. Instead of responding to the real stimulus, the impression has a tendency to adapt to the object as it is or is imagined to be.

The ability to recognise things in a variety of situations, which appear to be "taken into account" throughout a process of mental rebuilding of the known image, is a result of perceptual constancy. For instance, snow appears white in both the dim moonlight and the 800,000-fold brighter day. Reduced contextual cues that help with object identification and limited experience with the object both affect perceptual constancy.

Learn more about constancy here:

https://brainly.com/question/16926291

#SPJ2

Other Questions
Figure A is a scale image of figure B.Pls help!!! 2. Think about relative location. Where is europe located in relation to the united states? what about the location of new york state makes it a good location for trade between the united states and europe?. Terry's father is 76 inches tall. Terry's height is 75% of that height of his father. How tall is Terry? Can someone please help !! PLS HURRY LESS THAN 5 MIN Which elements are least likely to be used by an author to develop an idea in a personal narrative?A.situation and conflictB. descriptions and reflectionC.dialogue and interaction theD.research and statistics valores que comunica la cancion a que le tiras cuando sueas mexicano 7 increased by a number wAn expression is What is the reason for each step in the solution of the equation?18x 2x = 4xMatch the reasons with each step in the equation.Given 4. What was the final destination of all of Burgoyne's troops? A. Bennington B. Bemis Heights C. Saratoga D. Albany a store is having clearance sale where merchandise on the sales racks is reduced by 80% from the original price. if a jacket was originally priced at $76, what is the sale price? b) Give an example of an animal with radial symmetry and an example of an animal with bilateralsymmetry. (2 points) What safety standard did David M. Theno implement at Jack in the Boxrestaurants after the E. coli outbreak in 1992? Ivanna drove 420 miles using 18 gallons of gas. At this rate, how many gallons of gas would she need to drive 357 miles? What's a recycling plant and how are electromagnets used there? What is the net force on a car with a mass of 1000 kg if itsacceleration is 35 m/s^2? 1. When you look over a poem's formal ...... you may find clues about its tone and meaning. Learning Task 4: Write five good things for each of the following: Home, School and Community. Have your parents sign on your list. Follow the given format below. Do this in your answer sheet Good things done for home, school and community 1. 2. 3. 4. 5. how to find inflection points from first derivative if the dna sequence is TAC CCC AAG CTC GGT ATC. what is mRNAtRNAAA? Which of the following statements about car insurance is true?