Experiment 3: Wavelength and Frequency

Introduction:
This experiment was conducted in order to identify a mathematical relationship between wavelength and frequency in a wave. The current theory is that the equation  serves as a relationship between wavelength and frequency, where "v" is the speed of sound. Theoretically, the frequency and wavelength of a wave are inversely proportional.

Data:

Measurement of the wavelength.

Example of wave propogation using fundamental frequency at a wavelength of 2 meters.

Excel table of the characteristics of a wave with various wavelengths and using the fundamental frequency.

A graph of a wave's wavelength and frequency. This shows an inversely proportional relationship between the two.

Results/Conclusion:

Our graph and results table show a clear relationship between the wavelength and frequency of a wave. Both sets of data show an inversely proportional relationship between wavelength and frequency. Our data could have been affected by the fact that a change in the tension in the wave affects the frequency at which a wave propagates. Our data could have also been affected by the reliability in our equipment such as our use of the measuring sticks and the stopwatches used to measure the period of the wave. 

Experiment 5: Introduction to Sound

Introduction: 
This lab was conducted in order to analyze the sound waves produced by a human voice and a tuning fork. A microphone was used to gather the information.

Data:
#1 graph

Close up of the voice graph.

#1h graph

Graph given by LoggerPro using a human voice and recording for 0.3 seconds.

#2 graph

Graph given by a second voice by LoggerPro that is recorded for 0.03 seconds. 

#3 graph

Graph given by LoggerPro using a 440 Hz tuning fork and recording for 0.03 seconds. The graph is sinusoidal.

Results:

Voice graph #1

1) The wave is a periodic function. The graph shows repetition after some time.

2) About 5 waves are shown in this sample of 0.03 seconds. We determined this number by counting the number of maximum points present in the sample.

3) The probe collected data for about the time it takes to blink. 

4) The period of these waves is 0.008 seconds. We determined this by finding the amount of time it took to repeat the maximum points.

5) The frequency of the wave is 125 Hz. We determined this by using the equation f= 1/T where T is the period. 

6) The wavelength is 2.74 meters. The length of the sound waves is about as long as a table.

7) The amplitude of the waves is 2 arbitrary units of sound pressure. We determined the amplitude by subtracting the highest point from the lowest point.

8) The graph would likely be very cramped and not easily interpreted because the sample size would be large and the motion of the waves is very erratic.

Voice graph #1h

Comparison between the second voice graph and the first voice graph. Sample sizes are both 0.03 seconds.

Tuning fork

Comparison between the voice graphs and the tuning fork graphs. Sample sizes were both 0.03 seconds.

If we were to test our data for the same tuning fork at a quieter sound level, we would expect to have a smaller wave amplitude due to there being less pressure exerted by the tuning fork to the surrounding medium. We would produce this sound by hitting the tuning fork softer against a surface. By doing so, the amount of force exerted on the tuning fork by the surface will be less, which will decrease the intensity of the sound waves. 

Experiment 4: Standing Waves

Introduction:
This lab was conducted in order to understand the effect that an external force has on a standing wave.

Procedure:

The setup of the lab

Oscillate the string like so

Create oscillations for up to 10 harmonics for case 1, then repeat the procedure for the first 6 harmonics with 1/4 of its value.

Data:

Case 1:

Tension = 200g * 9.8 = 1.96 N

Mass of string = 0.74g

μ=0.000308kg/m

Nodes	Frequency (Hz)	Length (m)	Amplitude	Wavelength	1/λ
1	31	1.326	4.500	2.652	0.377
2	61	0.663	2.250	1.326	0.754
3	92	0.442	1.500	0.884	1.131
4	122	0.332	1.125	0.663	1.508
5	153	0.265	0.900	0.530	1.885
6	184	0.221	0.750	0.442	2.262
7	215	0.189	0.643	0.379	2.640
8	245	0.166	0.563	0.332	3.017
9	276	0.147	0.500	0.295	3.394
10	307	0.133	0.450	0.265	3.771

This shows the relationship between the frequency and wavelength when the string has a tension of 1.96N

Case 2: 

Tension = 50g * 9.8 = 0.49N

Mass of string = 0.74g

μ=0.000308kg/m

Nodes	Frequency (Hz)	Length (cm)	Amplitude	Wavelength	1/λ
1	15	1.326	1.100	2.652	0.377
2	31	0.663	0.550	1.326	0.754
3	46	0.442	0.367	0.884	1.131
4	62	0.332	0.275	0.663	1.508
5	77	0.265	0.220	0.530	1.885
6	93	0.221	0.183	0.442	2.262

This shows the relationship between the frequency and wavelength when the string has a tension of 0.49N

Analysis:

Wave velocity case 1

From graph:

v = 81.39 m/s

From equation:

v = 79.77 m/s

Wave velocity case 2

From graph:

v = 41.22 m/s

From equation:

v = 39.87 m/s

Ratio of wave velocities

From graph:

Ratio = 81.39/41.22 = 1.975

From equation: 

Ratio = 79.77/39/87 = 2.001

The ratios of wave velocities are very similar.

Number of harmonics	nf1 (Hz)
1	31
2	62
3	93
4	124
5	155
6	186
7	217
8	248
9	279
10	310

Ratio of frequencies

Ratios of harmonics	n	Case 1	Case 2	Ratio
	1	31	15	2.1
	2	61	31	2.0
	3	92	46	2.0
	4	122	62	2.0
	5	153	77	2.0
	6	184	93	2.0

The ratios for each comparable frequency are very similar. They have a ratio between 2.0-2.1. This is evident through the experimental results because when the tension was reduced to 1/4 its original value, the velocity doubled. 

This concludes that the velocity of a wave is proportional to the tension on the string. Our error could be attributed to measurements and the reliability of the equipment used.