Apparatus notes,

• Do not "over-drive" the string. Experiment with the amplitude to find the smallest amplitude that will give clearly visible resonances.
• If the hanging mass is too low, the resonance Q becomes, and resonances are indistinct.
• Try to stay within the range from 1 Hz to 100 Hz if possible. Resonances become harder to find at a high frequency. This means avoid very high masses.
• The function generator frequency adjustment is very delicate. Students must use a light touch.
• To simplify the estimation, we assume that there is no error regarding the measurement of time or frequency.

1, First make some basic measurements.

Please refer to Lab 1 of Phys40A, Lab 1 of Phys2A LAB, or Lab 2 of Phys 2C LAB, for the definations and examples of Accuracy and Precision.

The errors on m are dominated by

(a). Thick white -- String length uncertainty (it stretches)

(b). Thin white -- Mass uncertainty (least count on scale)

Therefore, you may estimate the errors on m and put them in the above table!

Question at Page 31 of Phys 40B:

Calculate from , Estimate the %error in this value.

Requirement:

• (0.5 POINT) Estimate the precision of the line density, m, of the thick sample strings, NOT ACCURACY! Put it in the last column of the above table.
• (0.5 POINT) Calculate the precision of v_Theory with respect to the thick string.
• (0.5 POINT) Estimate the precision of the line density, m, of the thin sample strings, NOT ACCURACY! Put it in the last column of the above table.
• (0.5 POINT) Calculate the precision of v_Theory with respect to the thin string.

Measurement of the standing wave on the thick string:

• L is the distance from the center of the mechanical drive to the center of the pulley.
• L _{from the center of the mechanical drive to the center of the pulley} = (        ), CGS Unit:(        )
• All given numbers of measured data are for your reference only. You have to correct them into the right value with significant figures if you think any of those numbers is incorrect!

Thick String - Resonant Frequencies, CGS Unit:(    )
Numbers of Resonance	Hanging Mass, CGS Unit: (    )
	255	105
2, (Optional)
3,
4,
5,
6,
7, (Optional)

The data for a hanging mass of 25 grams were very indistinct; i.e. low Q. The fundamental was not measurable. Masses below 50 grams should be avoided at this stage.

• The data for "f_n versus n" can be fit using Graphical Analysis.
• Print out the two graphs of "f_n versus n" with every proper indication, like hanging mass.
• Here you may assume that gravitational constant, g= 9.80´10²(cm/sec²)

Thick String - Wave speeds, v , CGS Unit:(    )
Hanging Mass, UNIT: (    )	255	105
Slope, Unit:(Hz)
vExp = 2L´ (Slope), CGS Unit: (    )
F = mg, CGS Unit: (    )
vTheory = , CGS Unit: (    )
ACCURACY in v's	%	%

Measurement of the standing wave on the thin string:

• L is the distance from the center of the mechanical drive to the center of the pulley.
• L _{from the center of the mechanical drive to the center of the pulley} = (        ), CGS Unit:(        )
• All given numbers of measured data are for your reference only. You have to correct them into the right value with significant figures if you think any of those numbers is incorrect!

Thin String - Resonant Frequencies, CGS Unit:(    )
Numbers of Resonance	Hanging Mass, CGS Unit: (    )
	205	105
2, (Optional)
3,
4,
5,
6,
7, (Optional)

 

• The data for "f_n versus n" can be fit using Graphical Analysis.
• Print out the two graphs of "f_n versus n" with every proper indication, like hanging mass.
• Here you may assume that gravitational constant, g= 9.80´10²(cm/sec²)

 

Thin String - Wave speeds, v, CGS Unit:(    )
Hanging Mass, UNIT: (    )	205	105
Slope, Unit: (Hz)
vExp = 2L´ (Slope), CGS Unit: (    )
F = mg, CGS Unit: (    )
vTheory = , CGS Unit: (    )
ACCURACY in v's	%	%

Additional Question: Please write down a simple conclusion of the whole Lab 5.

Requirement:

(0.5) Write it in no more than 4 sentences.

(0.5) Use some of your data tables, graphs and answered questions to make some quantitative argument.

Appendix:

Supplemental criteria for the above Question:

Assume <A>, <B> and <C> are mean values, s _A, s _B and s _C are the errors respectively. Then, we may write:

A = <A> ± s _A, B = <B> ± s _B, and B = <C> ± s _C.

Therefore, statistically,

1, If C = A ± B, then <C> = <A> ± <B>, and s _C²= s _A² + s _B².

2, If C = A ´ B, then <C> = <A> ´ <B>, and = + .

3, If C = A ¸ B, then <C> = <A> ¸ <B>, and = + .

4, If C = A^pB^q, then <C> = <A>^p<B>^q, and = p² + q² .

Therefore, if m = Mass ¸ Length, then <m > = <Mass> ¸ <Length> and (s _m /<m >)² = (s _Mass/<Mass>)² + (s _Length/<Length>)².

If you have an experimental value, C, only, %error = ´ 100%. Here, we do not know the theoretical value. <C> is the average of several measured values for C. And, s _C usually serves as an error, like, SDOM, the least count on scale, or any other systematic error.

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