Experiment 4: Standing Waves

Purpose: To understand the characteristics of standing waves in resonance driven by an external force(oscillator)

Equipment:

• 2.00 meters of string
• Mechanical Vibrator
• Function Generator
• Pulley
• Table Clamps
• 50 g and 200 g Counterweight
• Two-Meter Stick

Experiment:

 

Video of the laboratory procedure and set up

(pics of harmonic string waves hard to capture)

A 200g counterweight was positioned at the end of  2.00 meters worth of string onto a pulley. This was then string as extended across the able to a ring stand on its opposite end.

0.00083	Mass of String (g)
2.495	Length of String (m)
0.0003327	Linear Density (kg/m)
1.800	Effective String Length (m)

The function generator to the mechanical vibrator was placed on the the string, propagating a sinusoidal wave.

The generator was adjusted until the string oscillated in its fundamental mode.

The number of nodes, length between nodes, wavelength, frequency and voltage were recorded, and repeat for  eight antinodes.


 Part A - 200g Counterweight

# of Antinode	Length Node to Node (m)	Frequency (Hz)	λ (m)	1/λ		Theoretical Speed
1	1.800	24	3.600	0.2778		86.40
2	0.910	44	1.800	0.5556		79.20
3	0.595	66	1.200	0.8333		79.20
4	0.450	88	0.900	1.1111		79.20
5	0.370	110	0.720	1.3889		79.20
6	0.310	131	0.600	1.6667		78.60
7	0.265	154	0.514	1.9444		79.20
8	0.225	177	0.450	2.2222		79.65
			Average Speed			80.08

 Part B - repeated procedure for 50g Counterweight

 

# of Antinode	Length Node to Node (m)	Frequency (Hz)	λ (m)	1/λ		Theoretical Speed
1	1.800	11	3.600	0.2778		39.60
2	0.900	22	1.800	0.5556		39.60
3	0.620	33	1.200	0.8333		39.60
4	0.470	44	0.900	1.1111		39.60
5	0.350	55	0.720	1.3889		39.60
6	0.315	66	0.600	1.6667		39.60
7	0.265	77	0.514	1.9444		39.60
8	0.225	88	0.450	2.2222		39.60
			Average Speed			39.60

Conclusion:

Experimental Values		Theoretical Values
78.771	Case 1 Speed (m/s)	80.08	Case 1 Speed (m/s)
39.600	Case 2 Speed (m/s)	39.600	Case 2 Speed (m/s)
1.989	Ratio Case 1 / Case 2	2.022	Ratio Case 1 / Case 2

The experimental values and theoretical values were at a 1.6% error. This is furthered re-enforced by the graphs of frequency vs 1/λ