Module ііі. Physics of oscillations and waves. Optics
LABORATORY WORK
Study of stationary waves properties. Determination of frequency of string oscillations
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The purpose of the work:
- to study properties of stationary waves;
- to determine frequency of proper oscillations of a string, phase velocity of a wave in a string
Devices and accessories:
installation for string oscillations studying
Task 1. To measure proper frequency of oscillations
1.1. Set string tension Р1, to measure the oscillation frequency of strings three times in which the string entered in one, two and four half wavelength. Enter the results into table 1.
Table 1
String tension Р, N |
Exp. No |
п = 1 |
п = 2 |
п = 4 |
Δf, Hz |
ε, % |
п = 1 |
п = 2 |
п = 4 |
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f1і, Hz |
f1ave, Hz |
f2і, Hz |
f2ave, Hz |
f2і, Hz |
f3ave, Hz |
f1th, Hz |
f2th, Hz |
f3th, Hz |
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Р1 = 0,2 N |
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Р2 = 0,3 N |
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Р3 = 0,5 N |
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1.2. Set string tension Р2, to measure the oscillation frequency of strings three times in which the string entered in one, two and four half wavelength. Enter the results into table 1.
1.3. Set string tension Р3, to measure the oscillation frequency of string three times in which the string entered in one, two and four half wavelength. Enter the results into table 1.
1.4. Write down characteristics of string:
diameter d = _________m;, length l = _________m; cooper density =______________kg/m3
1.5. Calculate theoretical value of string oscillations frequency according to the formula:
fth і
=
.
1.5. Compare the experimental and theoretical values of frequency.
Task 2. Calculate the errors of measurements of frequency f1.
- Determine mean arithmetic value f1ave.
where n =3 the quantity of measurements. Enter the results into table 1.
- Calculate deviation from average value:
- Calculate root-mean-square deviation for average value
- Get absolute error of
measuring average value multiplying the value
on the Student’s coefficient
for reliable probability
and number of experiments n
= 3,:
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- Fractional error of measurements average value of wavelength of supersonic wave:
%
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Write results of measurements in such a way
=_________Hz.
Task 3. Determination of wave phase velocity
3.1. Calculate experimental value of wave phase velocity for each mean value of frequency according to the formula
.
Table 2
String tension Р, N |
Exp. No. |
υi, m/s |
υi ave, m/s |
υth i, m/s |
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n = 1 |
n= 2 |
n = 4 |
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0,2 N |
1 |
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0,3 N |
2 |
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0,5 N |
3 |
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3.2. Calculate theoretical value of wave phase velocity according to the formula
υth i
=
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Enter the results into table 1.2.
3.3. Compare the experimental and theoretical values of wave phase velocity.
Task 4. Plot the graphs of dependence between wave phase velocity and string tension υth= f(P) and on the scaled paper using the data from table 2.
Conclusion:
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The data of laboratory work fulfilment _______________________________________________
Pass mark ________________________________________ Signature ______________________
Mark of laboratory work defence __________________ Signature _______________________
q
uestions
to be admitted for doing laboratory work
and its defending
1. What is the stationary wave?
2. Conditions for stationary wave creation.
3. Deduce the equation of stationary wave.
4. Deduce the equation for coordinates of nodes and antinodes of stationary wave.
5. How is stationary wave represented graphically?
6. Energy of stationary wave.
7. How is frequency of string proper oscillations determined if a sting is fixed on one end; on both ends; in the middle?
8. What is a basic tone and an overtone?
9. Demonstrate how frequency of string proper oscillations and the phase speed of stationary wave depend on string tension.
10. Describe the method of experimental determination of proper frequency of string oscillations.
LABORATORY WORK