Experiment 4: Standing Waves

Purpose:
To understand the characteristics of standing waves when in resonance and driven by an outside source. 

Equipment:

• String (2 meters)
• Pulley
• Mechanical Vibrator
• Function Generator
• Counterweight (50 g and 200 g)
• 2 meter Stick
• Various Lab Components



Experiment:

 

Attach a string to a ring stand on one side and over a pulley on the other. Place a 200 g counterweight on the end of the string. Connect the function generator to the mechanical vibrator and place it with the string passing just over the top closest to the end attached to the ring stand. Measure the effective distance (from mechanical vibrator to pulley) of the string. Adjust the function generator until the string oscillates in its fundamental mode. Record the number of nodes, the length between nodes, the wavelength, the frequency and voltage. Repeat for up to eight antinodes. Repeat entire experiment with 50 g counterwieght. 

 

 

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

 

Below is the data for the 200 g counterweight.

 

200 gram 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

Below is the data for the 50 g counterweight.

50 gram 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:

The theoretical value and experimental value ratios have a percent error of 1.6%. 

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