stationary wave dana santika fisika undiksha

7/30/2019 Stationary Wave Dana Santika Fisika Undiksha

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1 | S T A T I O N A R Y W A V E

STATIONARY WAVE

A. PURPOSE OF EXPERIMENTThere are some purposes which want to be achieved from this experiment.

1. Investigating the relationship between waves velocity through the tensionand the density of used string by Meldes Law.

2. Determining the density of used string by Meldes Law.

B. TOOLS AND MATERIALSHere are the tools and materials needed in order to do this experiment.

1. String (102.80 cm 1.03 m)2. Mechanical Wave driver3. Digital Function Generator (Amplifier)4. Table Fix Pulley5. Varied mass6. Ohaus Balance (SSN = 0.01 gram)7. Vibrator Board8. Ruler (SSN = 0.1 cm)

C. FUNDAMENTAL THEORYA wave is the propagation of a disturbance through a medium. The physical

pstringrties of that medium (e.g., density and elasticity) will dictate how the

wave travels within it. A wave may be described by its basic pstringrties of

amplitude, wavelength, frequency and period T. Figure 1 displays all of thesepstringrties. The amplitude,, is the height of a crest or the depth of a troughof that wave. The wavelength, , is the distance between successive crests orsuccessive troughs. The time required for a wave to travel one wavelength is

called the period, . The frequency,, is 1 , and is defined as the numbercycles (or crests) that pass a given point per unit time.


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Figure 1. Pstringrties of Wave

Since the wave travels one wavelength in one period, the wave velocity is

defined as . The wave velocity can then be written as follow.

v = f ...................................................................................................... (1)Where:

v = wave velocity (m/s)

= wavelength (m)

f = frequency (Hz)

In this experiment, we will introduce an oscillating disturbance to a length of

string with the use of an electric vibrator. The vibrator shakes the string back

and forth, creating a disturbance perpendicular to the string's length. Thisdisturbance, then, propagates along the string until it hits the stationary pulley

about one meter away. This wave is known as a transverse wave since its

disturbance is perpendicular its motion. When the wave reaches the pulley-end

of the string it is reflected back toward the vibrator-end of the string. In doing

so, the disturbance is not only reflected back along the string, but it is also

reflected over the axis of propagation. This is shown in the figure.

Figure 2. Wave Reflection


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When a vibrating body produces waves along a tightly stretched string, the

waves are reflected at the end of the string which cause two oppositely

traveling waves to exist on the string at the same time. These two waves

interfere with each other, creating both constructive and destructive

interference in the vibrating string. If the two waves have identical amplitudes,

wavelengths and velocities, a standing wave, or stationary wave, is created.

The constructive and destructive interference patterns caused by the

superposition of the two waves create points of minimum displacement

called nodes, or nodal positions, and points of maximum displacement

called antinodes. If we define the distance between two nodes (or between two

antinodes) to be , then the wavelength of the standing wave is = 2.Figure 3 illustrates the case where the length of string vibrates with 5 nodesand 4 antinodes.

Figure 3. Stationary Wave

The wave velocity of a standing wave is dependent on the medium through

which the wave travels. The velocity of standing waves propagating through ataunt string, for instance, is dependent on the tension in the string, , and thelinear density of the string, . For waves of small amplitude this velocity isgiven by this formulation.

Tv ..................................................................................................... (2)

Where:

v = wave velocity (m/s)
http://www.clemson.edu/ces/phoenix/labs/224/standwave/10.jpghttp://www.clemson.edu/ces/phoenix/labs/224/standwave/10.jpg


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T = string tension force

= string mass per unit length (kg/m).

Based on the equation (1) and (2) price obtained by the strings of a given

frequency as follows:

Tf

1 ............................................................................................. (3)

For the basic node (n = 1), obtained L = or = 2L

For the tone of the first (n = 2), obtained L =

For the tone of the second (n = 3), obtained L = 1 or = 2/3 L

In general, the relationship with L can be written as follows.

n

L2 ..................................................................................................... (4)

Where;

n = 1, 2, 3, .

L is the string length.

D. EXPERIMENT METHODThe following are the experiment method that should be done in order to do

this experiment.

1. Arranging the equipment as shown in figure below.

2. Using the smallest density of wire connector or medium load and hangapproximately 50 grams or more. Record (mass per unit length of wire),

L (length of wire from the tip of the clamp down to the pulley / wire that

form the wave), and m (mass) the total hanger.

1 2

3

4

51. Amplifier2. Vibrator3. String4. Pulley5. Block Mass


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3. Changing the frequency of amplifier for got at least 2 standing wavepattern (n = 2). For each pattern, note the n-level mode (n = 1 each ),

then measure the frequency (f) and wavelength ().

4. Repeating steps above by changing the frequency regulator for n = 3 and n= 4.

5. Repeating the experiment and calculations in step 2 till with 4 by changingthe load from 50 grams to a maximum of 120 grams. Do as much as 5

times the data. For every change of note hanging mass (m) and tension (T)

6. Record your observations in the following table.L =.................. g = 10 m/s2

No m (gr) T = m g (N) n f (Hz) (m)

1 2

3

4

2 2

3

4

N

E. DATA ANALYSIS TECHNIQUEData obtained on the stationary wave experiments on strings with variations m

used to find the relationship between velocity v and the tension T. As a basic

analysis is the equations 2) that in other forms are:

T = avgv2 ........................................................................................ (5)

With vavg an average value of v. Equation (4) is identical to the simple linear

regression equation

Y = a + bX ......................................................................................... (6)

With constant a = 0. Thus, the data analysis used simple linear regression

analysis technique based on the principle of least squares as a result of

modification of equation (7), namely:

Yi = bXi ............................................................................................... (7)


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With Yi = T and Xi = v2

avg, each of these states and the square of the average

load voltage wave velocity of each of these loads are measured. Based on the

equation (4) and (6), then the constant b satisfies the equation is obtained from

b =

22

ii

iiii

XXN

YXYXN.............................................................. (8)

N is the number of variations of T as a function v 2avg. Standard deviation (b)

is determined by the equation:

22

ii

y

XXN

NSb

.............................................................. (9)

Sy is the best estimate for the value ofb of the straight line Y i = bXi which

can be calculated using the following equation:

22

222

222

2

1

ii

iiiiiiii

iy

XXN

YXNYYXXYXY

NS .......... (10)

The result of measurement is tolerable if the value of the relative error is

smaller than 10%.

F. DATA OF EXPERIMENTNo Mass (gr) T = m g (N) n f (Hz) (m)

1 50.20 502.0

2 50.2 1.03

3 75.8 0.69

4 100.1 0.52

2 60.59 605.9

2 52.4 1.03

3 81.3 0.69

4 106.5 0.52

3 70.20 702.0

2 54.7 1.03

3 86.8 0.69

4 114.0 0.52

4 80.19 801.92 56.2 1.03

3 79.7 0.69


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4 109.1 0.52

5 100.52 1005.2

2 67.1 1.03

3 97.8 0.69

4 133.9 0.52

G. DATA ANALYSISWe could know the tension of string by equation = . and the length ofwave from = 2

.No m (kg) T n f(Hz) (m) =. vavg1 0.0502 0.5020

2 50.2 1.03 51.706

52.023 75.8 0.69 52.302

4 100.1 0.52 52.052

2 0.06059 0.6059

2 52.4 1.03 53.972

55.153 81.3 0.69 56.097

4 106.5 0.52 55.38

3 0.0702 0.7020

2 54.7 1.03 56.341

58.503 86.8 0.69 59.892

4 114.0 0.52 59.28

4 0.08019 0.8019

2 56.2 1.03 57.886

56.543 79.7 0.69 54.9934 109.1 0.52 56.732

5 0.10052 1.0052

2 67.1 1.03 69.113

68.743 97.8 0.69 67.482

4 133.9 0.52 69.628

The relations between tension (T) and velocity of wave (v).

T (N) Vavg (m/s)

0.5020 52.020.6059 55.15

0.7020 58.50

0.8019 56.54

1.0052 68.74


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The Relationship Graph of Tension (T) and Velocity (V)

From the graph above, the relation between Tensions of string (T) with

velocity of the wave (v) is proportional. If the tension is enlarged, the velocity

of wave will also be greater at a value of and vice versa. We can determine

the error with the regression linear equation, when 2 = and T = Y, so wecan make the table below.

No 2 = T=Y X2 Y2 XY1

2706.08 0.52 7322871.131 0.2520 1358.452 3041.486 0.6059 925635.467 0.36711 1842.84

3 3422.757 0.702 11715265.61 0.4928 2402.78

4 3196.432 0.8019 10217179.89 0.6430 2563.22

5 4725.325 1.0052 22328697.12 1.0104 4749.90

17092.08 3.617 60834649.22 2.7654 12917.20

1. Determining the constant b

22)(

))(()(

XiXiN

YiXiXiYiNb

= 512917.20 (17092.08)(3.617)560834649.22 (17092.08)2

= 2.3 104

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

50 55 60 65 70

Tension

(T)

Velocity (V)


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2. Determining Sy2 = 12 2 2()22 +( )2 2()2 2 = 152 2.7654 60834649 .22(3.617)2217092.0812917 .203.617+5(12917 .20)2560834649 .22(17092 .08)2 2 = 0.007300588 = 0.085443478

3. Determining

= 2 ()2 = 0.085443478 5

560834649.22 (17092.08)2 = 5.5 105

4.Determining the density of the string () = = 2.3 104 5.5 105 = (2.3 0.6) 104/

5. Determining Relative Error (RE) = 100%

=0.6 10

4

2.3 104 100% = 26 %


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H. DISCUSSIONAccording to the data analysis, it is retrieved the following results.

a. Waves velocity for each variety of mass and tension is shown below.m (kg) T (N) Vavg (m/s)

0.05020 0.5020 52.02

0.06059 0.6059 55.13

0.07020 0.702 58.50

0.08019 0.8019 56.54

0.10052 1.0052 68.74

The table shows that the tension (T) has a linear relationship with the

velocity of wave (v). Because the tension is dependent to the mass,

indirectly the mass also has a linear relationship to the velocity of wave. It

means that if the mass being bigger, then the tension is going to be bigger,

and finally, the velocity of waves will be bigger. In the contrary, if the

mass is being smaller, then the tension of string will be smaller, and finally

the velocity of wave is also being smaller.

b. The density of string () retrieved from the experiment is (2.3 0.6) 104/ with the relative error (2) = 26 % which shows us that theresult of experiment is unacceptable since the value of(2) is more than10%.

It is believed that there are some errors that inflences to the final of this

experiment.

1. Common ErrorCommon error is error that occurs because of the human error. The

common error of this experiment is the parallax error in the reading scale

of Ohaus balance and the scale of vibrator (frequency). In other way, the

students are unskilled in using the certain instrumental such as the vibrator

and ohaus balance.

2. Systematic ErrorSystematic error is an error that occurs because of the instruments used as

the influence of the environment at the time of trials. The systematic error


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of this experiment is caused by the connectror cables which did not work

well, then it influenced to the value of frequency.

3. Random ErrorRandom error is an error which the causing factors are uninvestigated. The

random error of this experiment is the fluctuation of temperature, magnetic

field, vibration of air, etc.

I. CONCLUSION AND SUGGESTION1. Conclusion

The following are the conclusions related to the result obtained from the

experiment.

a. The tension (T) has linear relationship with the velocity of wave (v). Itmeans, increasing tension with increase the mass of weights it would

increase the velocity and vice versa.

b. The density of string () retrieved from the experiment is (2.3 0.6) 104/ with the relative error (2) = 26 % which shows us thatthe result of experiment is unacceptable since the value of (2) ismore than 10%.

c. The result of this experiment is unacceptable since there are some errorsoccurred during the experiment. They are the common errors,

systematic errors, and random errors.

2. SuggestionThe suggestion that can be provided to the readers and other human in

order to do the same experiment is checking the necessary equipment anddecrease the value of common error. Are the tools and the materials used

still eligible to use or not. If actually it still can be used, then use them well,

but if the tool used is in not good condition, then it is recommend to replace

it with the good others because it will affect the final results of the

experiment. It may be useful to use the unit ofdynes rather than Newtons

when measuring the tension force. Note that 1 = 1 2 = 105.


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REFERENCES

Giancoli, Douglas C. 2001. Physics Fifth Edition Fascicle 2. Jakarta: Erlangga

Suardana, I Kade. 2007. The Laboratory Physics Lab Work III . Guiding Book of

Physics Laboratory 3, MIPA Faculty, Ganesha University of

Education.

Supiyanto. 2002. Physics Junior High School. Jakarta: Erlangga.

Sutedjo&Purwoko. 2005. Physics Technology and Industrial. Jakarta: Yudhistira.

stationary wave dana santika fisika undiksha

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