Standing Waves

Objective

Determine the right relationship between spring length, velocity to create a standing wave with different frequency.

Procedure

SET UP THE FREQUENCY GENERATOR

SET UP THE MASS

OBSERVE THE STANDING WAVE

 Data

		Length (m)	Mass (kg)	Density (μ, kg/m)
	String	1.98	0.00061	0.0003087
	Case #1	Length (L)	Hanging mass (kg)		Tension	Wave Speed
		1.45	0.20		1.96	79.72
		# of wave (n)	Frequency (Hz)	wavelength (λ)	1/λ
		1	28	2.90	0.34
		2	56	1.45	0.69
		3	83	0.97	1.03
		4	111	0.73	1.38
		5	138	0.58	1.72
		6	167	0.48	2.07
		7	194	0.41	2.41
		8	222	0.36	2.76
		9	249	0.32	3.10
		10	277	0.29	3.45
	Case #2	Length (L)	Hanging mass (kg)		Tension	Wave Speed
		1.45	0.050		0.49	39.86
		# of wave (n)	Frequency (Hz)	Wavelength (λ)	1/λ
		1	14	2.90	0.34
		2	28	1.45	0.69
		3	39	0.97	1.03
		4	47	0.73	1.38
		5	70	0.58	1.72
		6	84	0.48	2.07

 CASE 1

Graph 1/lambda vs f

the slope is the wave speed

CASE 2

Graph 1/lambda vs f

the slope is the wave speed

The ratio of the frequencies to same harmonics:

Conclusion
Since v is proportional to tension, we made the tension in case 2 four times bigger than case 1, so we should get the wave speed of case 2 two times faster than case 1. The wave speed of case 2 was about 2.06 times faster than case 1, which is what we expected. And we also got the same ratio of frequency in different modes. This experiment was very successful.