Experiment 4 wave(2)

Purpose:




the purpose of this lab is to analyze the element of wave, such as wavelength, frequency, wave speed, tension, and period. and figure out what is the relationship among then. how does these element affect the wave.


Experiment Equipment:


Pasco Variable Fequency Wave Driver with string, Pasco Student function generator, counterweight, pulley, digital multimeter, 1 or 2 meter stick, short rod.



Experiment Data:


we measure the length of the string: 1.53 m, the weight of the string is 1.8 g = 0.0018 kg.


so we get the linear density of the string u = 0.0018kg / 1.53 m = 0.00117 kg/m


then the experiment divide into two part in different tension



we use counterweight is 300 g = 0.3 kg, T1 = 0.3 * 9.8 = 2.95 N

Tension 1 = 2.95N

Tray	Wavelength /m	Frequency /Hz	Distance between the node/m
1	3.06	13.6	1.53
2	1.60	27.0	0.80
3	1.04	40.7	0.52
4	0.74	56.1	0.37
5	0.71	69.3	0.31
6	0.52	81.3	0.26
7	0.43	99.4	0.22

speed of wave v = sqrt( T/u ) = sqrt( 2.95 / 0.00117 ) = 50.02 m/s.



then we plot the frequency of the wave versus 1/wavelength in excel to get a graph:

the slope of the graph is 43.01 which very close to the speed of the wave v = 50.02 m/s.

for the second part of the experiment, we reduce the tension, we use 200 g = 0.2 kg, tension = 0.2 * 9.8 = 1.97 N

Tension 2 = 1.97 N

Tray	Wavelength /m	Frequency /Hz	Distance between the node/m
1	3.06	16.8	1.53
2	1.56	33.8	0.76
3	1.00	51.0	0.50
4	0.74	67.2	0.37
5	0.60	85.8	0.30
6	0.49	103.6	0.25
7	0.45	120.6	0.22

from equation wave speed v = sqrt( T / u ) = sqrt( 2.97 / 0.00117 ) = 50.38 m/s

we plot the frequency ofthe wave versus 1/wavelength to get a graph:

we get the slope is 52.043 which is very close to the wave speed we get from equation above.

ratios of wave speeds for case 1 compared to 2(experiment wave speeds) = 43.01/52.04 = 0.83.

ratios of wave speeds for case 1 compared to 2( predicted wave speeds) = 50.02 / 50.38 = 0.99.

the two ratios are close, but not the same.

the measured frequencies for case 1 equal to nf1, where n is the number of the harmonic

27/13.6~2

40.7/13.6~3

56.1/13.6~4

69.3/13.6~5

81.3/13.6~6

99.4/13.6~7

the ratio of the frequency of the second harmoic for case 1 compared to case 2.

16.8 / 13.6 = 1.24

33.8/27=1.35

51/40.7=1.25

67.2/56.1=1.20

85.8/69.3=1.25

103.6/81.3=1.27

120.6/99.4=1.21

we take look at all the data of the ratio of the frequency of the second harmonic for case 1 compared to case 2, all the ratio are closed to 1.25, the reason have these variable ratio because the when we do the experiment, we have so many error percent, so make the data are not 100% acurate.

Conclusion:

from this experiment, we get that when the length of the string and the tension of the string is stable, the wavelength will decrease by the frequency increase. and the speed of the wavelength is independent of the frequency is only depend on the tension and the linear density of the string. after the experiment, we do the data analyze, and calculate all he ratio requirement by the experiment. and measured frequencies for case 1 is mostly equal to nf1, and the ratio of the wave speeds for case 1 compared to 2 is mostly equal to the ratios of the predicted wave speeds. but our experiment have error such as we measure the lenght of the string, or determine the perfectly wavelenght frequency is not exact. but overall our experiment make sense.