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