Mind Map of Vibrations and Waves

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Exercise on Chapter 18

14. If 20,000 waves are performed in 2 minutes, then the period is . . .

Answer:
F = 20,000  = 166.7 Hz
         120
P =    1    s
      166.7

15. Look at the following figure of a wave.
                                                                      t = 10 s                      
                                                 |                                                      |

The frequency of the wave is . . .

Answer:

F =   1   = 0.1 Hz

       10

16. The frequency of a wave is 200 Hz. If the velocity of the wave is 400 m/s, the wavelength is . . .

Answer:

Wavelength = velocity  = 400  = 2 m 

                      frequency   200

17. Look at the following figure of a transverse wave.

With the frequency of 50 Hz and wavelength of 1 m, the velocity of the wave is . . .

Velocity = wavelength x frequency

               = 1 x 50 = 50 m/s

18. If one complete wave consists of one compression and one expansion part, then the name of the wave is . . .

Answer: Longitudinal wave

19. The velocity of a wave is 100 m/s and its frequency is 150 Hz. The wavelength is . . .

Answer:

wavelength = velocity   = 100  = 0.67 m

                      frequency   150

20. Sound propagates in the air with a speed 350 m/s. If the frequency of the keynote a is 450 Hz, then the wavelength is . . .

Answer:

wavelength = velocity  = 350 = 0.78 m

                      frequency  450 

Vibration and Waves Worksheet

1. Known that a spring-mass system has
Vibration  = 20 times/s
Frequency= ?
                 = n  = 20 = 20 Hz
                     t       1
Period       = ?
                 = 1  = 1 seconds = 0.05 seconds
                     f    20

2. Known that a period of a pendulum is 0.40 seconds
a) Find the frequency
Frequency= 1  =   1     = 2.5 Hz
                    T     0.40
b) Times passing the lowest point in 1 second
= 2.5 times = 5 times (1 vibration will touch the lowest point 2 times)
c) Times passing lowest point in 7 seconds
= 5 x 7 = 35 times

3. Known that...
- 10 vibrations in 6 seconds
- amplitude = 4 cm
a) Find the frequency and period
F = n  = 10  = 1.67 Hz
       t       6
P = 1  =   1   = 0.15 s
       f     1.67
b) The amplitude is 4 cm. Find the period and frequency.
- Same answers as in 3(a) -

4. Known that there are 25 oscillations/50s. Find the frequency and period.
F = n  = 25  = 0.5 Hz
       t      50
P = 1  = 1   = 2 seconds
       f     0.5

5. Known that the distance is 0.40 m and the object vibrates 25 times/min.
a) Find the amplitude
= 0.40 m  = 0.2 m
       2
b) Find the frequency
= n  = 25  = 0.417 Hz
    t      60
c) Find the period
= 1  =     1     = 2.4 s
    f      0.417
d) Find the amplitude if it is 2 meters
= 2 m  = 1 m
     2

6. Known that the frequency of an object is 260 Hz and the wavelength is 1.5 m. Find the velocity of that object.
= wavelength x frequency = 1.5 m x 260 Hz = 390 m/s

                                                                                   -8                                                    9
7. Known that the wavelength of an object is 6 x 10  m and the speed is 4 x 10  m/s
Find the period and frequency.       9                         17
Frequency =   velocity    =  4   x 10  = 0.67 x 10
                     wavelength    6       10-8
Period =  1  =      1         17 = 1.5 seconds
                f       0.67 x 10
                                                                       
8. Known that the velocity of an object is 12 m/s and the frequency is 2 Hz. Find the wavelength.
velocity = wavelength x frequency
wavelength=   velocity    = 12  = 6 m
                      frequency       2

Velocity of Wave

A wave has a velocity when a vibrating object is not moving or propagating from one place to another. The velocity of a wave defines how fast a wave propagates.

The two formulas of velocity are as follows:

1. v =      λ (wavelength)             /     s (distance to be covered)

           t (period of the wave)                   t (covering time)

2. v =  λ (wavelength) x f (frequency)

Questions including answers of the two formulas:

2nd Formula

  The velocity of a wave is 50 m/s. If the wavelength is 10 m, what is the frequency of that wave?

v = λf  so  f =  v 

                        λ

f =  50 m/s  = 5 Hz

       10 m

1st Formula

  Given: distance to be covered = 6λ

              time needed = 4 s

  Find:   velocity

v =  6  = 1.5 m/s

       4

Wave Properties

- A wave is a disturbance or vibration which propagates along a
medium. An example is the waves on a water surface.


- Mechanical wave is a wave that needs a medium in which the wave propagates. An example is waves in a rope, because they need media for their propagation.


- Electromagnetic wave is a wave that does not need any media to propagate. Such examples are signal of a cell-phone.


- Transverse wave is an element of a wave that is always in the form of a peak and valley. One complete wave has one peak and one valley. It is either on the rope, on water, or on slinky (long, flat spring made of steel).

- Longitdinal wave does not have peaks and valleys unlike transverse wave, instead, it has compression and expansion part. A complete wave has one compression and one expansion part. An example is vibration in gases.

- A wave length is the length of a wave consists of one peak and one valley.


http://www.dptips-central.com/light.html
http://wiki.answers.com/Q/What_are_the_example_of_longitudinal_waves
2B Science Book

Frequency, Period, and Amplitude

Frequency is the number which defines the number of vibrations performed by an object within one second. From this understanding, the unit of frequency of a vibration is "the number of vibrations per second" or hertz (Hz).

Period is the time needed to make one vibration. For example, if the frequency of a vibration of a pendulum is 1 Hz, then it means every vibration needs one second. This one second time is called the period of the vibration.

Amplitude is the farthest distance of displacement of a vibration. If we look at the figure on the bottom side, the amplitude is the distance between the movements.

Formulas:

The formula for frequency is the numbers of vibrations divided by time. F = n (vibrations) = ... Hertz

                                                                                                                         t (seconds)

The formula for period is one divided by frequency. T (symbol for period) =  1 = ... seconds

                                                                                  f

Questions and Answers:

1. A ruler on a table moved, performs 14 swings within 7 seconds. What is the frequency of that ruler?

F = n  = 14 vibrations = 2 vibrations/second = 2 Hz

       t       7 seconds  

2. If the frequency of a vibration is 20 Hz, what is its period?

T = 1  =  1  = 0.05 seconds

       f      20

Sources: 

- 2B Science 2nd Semester Grade VIII textbook

- http://www.calacademy.org/products/pendulum/page1.htm

- 

Vibration Motion

Examples of vibration motion:

A pendulum is an object hung by a string from a fixed support. When we displace the object from equilibrium, it moves back and forth around it's equilibrium position. This is called vibration.

There is a spring on a stand and load on the bottom. If we pull the load, there will be motion on the load hanging on the spring. This is called spring motion.






Vibration is something moving rapidly and continuously back and forth passing through the balance position.

Examples of vibration motion in real life:

- A bobblehead doll is an example. Once we push the head with our finger, it will continuously move around through the balance position until it stops.

- A spring horse is another example. When a child sits on it and either pulls or push the handle, it will move rapidly and continuously until it stops.

Sources:
http://www.physicsclassroom.com/class/waves/u10l0a.cfm
http://www.physicsclassroom.com/class/waves/u10l0c.cfm

Conservation of Mechanical Energy

CONCEPT

Mechanical Energy is the energy associated with motion. Mechanical Energy is divided into potential and kinetic energy.

Potential energy: the energy stored within an object.

For example, a stretched bow of an archer.

The formula for potential energy is
mass x gravitational acceleration x height

Kinetic energy: the energy possessed by the object because of its motion or because of its velocity.

For example, a person running.

The formula for kinetic energy is 0.5 x mass x velocity2





EQUATIONS + SOLUTION

Kinetic Energy
Determine the Kinetic Energy of a rabbit hopping with velocity of 2 m/s and 12 kg mass.
KE= 0.5 x m x v2
KE= 0.5 x 12 kg x 22
KE= 24 Joules

Potential Energy
Determine the Potential Energy of a chandelier hanging from the ceiling with a mass of 4 kg, hanging 5 m high and 12 m/s2 for the gravitational acceleration.
PE= m x g x h
PE= 4 kg x 12 m/s2 x 5m
PE= 240 Joules


CONSERVATION OF ENERGY

- It is the transformation from one form of energy into another.
- Instruments or objects which help the transformation are called converters.
- Example: a lamp turned on changes electrical energy into light and thermal energy.

Sources of Energy

  Sources of energy which are not renewable: cannot be regenerated after it is used up.
Examples are fossil fuel, coal, and natural gas.

  Sources of energy which are renewable: Source of energy which can be regenerated when it is used up.

 1. Wind Energy
- Always available in nature.
- Example: windmill. Disadvantages are they have big construction size and needs a high speed wind.


2. Waterfall Energy
- Moving water can rotate a turbine which further produces energy.
- Moving water has sufficient potential and kinetic energy.
- Example: Hydroelectric power plant. It is electricity generated from the energy of moving water.


3. Solar Energy
- Easy to get and pollution free
- It will never run out because the sun always beam to earth
- Example: calculator using solar energy



4. Nuclear Energy
- Fission: the splitting process of a heavy nucleus into two lighter nuclei and a huge energy release. Examples are nuclear power plant.
- Fusion: the process of joining the nuclei of atoms and a huge energy release.

5. Tidal Energy
- Example is a dike, used to gain electricity in a tidal power plant.

6. Geothermal Energy
- Produced from the heat of earth.
- A power plant which uses geothermal is called a geothermal power plant.

7. Biomass Energy
- The energy which comes from plants to animals.
- Plants are processed into alcohol to get biomass energy.

Self Assessment 15.6

1. Fossil fuels are considered as a source of energy which is not
renewable. Why is it so?
Fossil fuels take millions of years to form under the surface of earth, and when its burnt, they are finished.


2. What happens if the fuel consumption is not spared? 
When the fuel consumption is not spared, it will eventually run out and we will have to find alternatives.

3. Write down the dangerous issues of having a nuclear power plant. 
- Radioactive

 materials can come into contact with people mainly through accidents in nuclear power plants, accidents in transporting radioactive materials, and escape of radioactive wastes.

- 

Radiation can penetrate deep inside the human body where they can damage cells and thereby initiate a cancer. They can also cause genetic diseases in offsprings.

4. According to your opinion, in order to produce electrical energy, what is the best energy that fits with the current situation and is pollution free?
I think solar energy is the best energy that fits with the current situation. Solar energy is easy to get and it is pollution free and often noiseless. The sun will always beam onto Earth so this energy will never run out.

5. Write your suggestion in order to produce a very high temperature, so that a large amount of electricity can be generated from the use of seawater.

From the tidal energy of the seawater, we can convert it into electrical energy by putting a wave energy converter.

http://diditsmile.blogspot.com/2012/09/menghasilkan-energi-listrik-dari.html
http://www.physics.isu.edu/radinf/np-risk.htm
http://wiki.answers.com/Q/Why_are_fossil_fuels_considered_non-renewable

Chapter 3.1, Work

2. Work= F x D

             = 5000 N x 3000 m

             = 15 000 000 J

4. Work= F x D

    Distance= W ÷ F

                  = 20 000 J ÷ 340 N

                  = 58.82 m

6.  Mass= 100 kg

     Distance= 60 m

     Work= 1000 N x 60 m

              = 60 000 J

8.  Distance= 0.8 m

     Mass= 62 kg

     Work= F x D

              = 620 N x 0.8 m

              = 496 J

10. Force= 300 N

      Distance= 750 m

      Work=? 

(a) Friction=200N                                              (b) Friction= 300N

     W= (F1-F2) x d                                                  W= (F1-F2) x d

         = (300N-200N) x 750 m                                    = (300N-300N) x 750 m

         =  75 000 J / 75 kJ                                              = 0 J    

   

Energy

  People do work (running, walking, etc.) because they have energy. So, energy is defined as the ability to do work. The important thing about energy is that it is conserved, cannot be created or destroyed.

   For example, if object 1 hits object 2, the energy from object 1 goes to object 2 and the molecules in object 2 can cause the energy to vibrate, or go around the room, etc. The energy doesn't disappear.

Energy can come in different forms.

                         Chemical: Energy contained within food, your body, and fuel. The examples are gasoline filled up in a car, and batteries.

 Thermal: Vibration and movement of the atoms and molecules within substances. Some
examples are water boiled in a kettle and rubbing your hands until it feels warm.

                                 Sound: Energy created from the vibration of air particles around a sound source. Some examples are clapping your hands and a plane taking off.

 Light: Energy created by the radiation of electromagnetic waves. Examples are a
fire and the sun shining.

                                   Electrical: Energy created from the presence and flow of electric charge. Lightning is an example of electrical energy in nature and also stroking a cat with long fur.

 Nuclear: Energy released from the reaction of the radioactive matters. The examples 

are atomic and hydrogen bombs and also the sun (the energy is transmitted from sun

to earth in the form of electromagnetic radiation).

Mechanical: Energy associated with motion.

 1.  Potential energy, the energy stored within an object.

Spring potential energy - an archer's bow and a sling shot is two examples because 

when someone pulls it, energy is stored within it until it is released.

Gravitational potential energy - an apple hanging on a tree and a swing
are two examples. Both examples have gravitational potential energy because of the position.
The potential energy within the objects relates to its distance above ground.

2.  Kinetic energy, the energy possessed by an object because of it's motion/movement.

An object falling off of a table and a water falling from a tap water are some examples.

ball rolling down a slope
- kinetic and potential energy-

An apple hanging from a tree
-potential energy-

Resources:




- http://plainenglish.viewshare.net/physics/mechanics/energy.shtml
- http://www.nmsea.org/Curriculum/Primer/forms_of_energy.htm
- http://www.eia.gov/kids/energy.cfm?page=about_forms_of_energy-basics
- www.wisegeek.com/what-is-electrical-energy.htm

What is work?

Work involves force and displacement of objects. It can also be defined as a transfer of energy. So to do work, there are some requirements:
- a force must cause displacement
- a force must have the same direction as displacement

The formula of work is force times distance because work is the application of a force over a distance.
(Force: W x D)
The unit of measurement for force is N (Newtons), distance is m (meters), and work is J (Joules).

Examples of work:
1. A woman is pushing a trolley. She transfers force to the bed until it moves, so it is considered as work.
2. Two men are lifting a box from the floor, they are producing force so the box is lifted.

Sources:
 http://www.edinformatics.com/math_science/work_energy_power.htm