Experiment 5: Sound Wave

Purpose:

        The purpose of this lab is to study the characteristics of sound waves.

Materials:

Materials needed in this lab is a logger pro, sound sensor, and a tuning fork.

Equipment Used

Procedure:

1. 

First person saying "AAAAAAA" into the microphone to record the first sound  wave.

2.

Second person saying "AAAAAA" into the microphone to record the second sound wave

3.

Strike the tuning fork

Record the sound wave into the microphone to record the third sound wave

4. Repeat step 3, but strike the tuning fork softer to create a softer voice. This will be the fourth sound wave.

Data and Analysis:

1. First sound wave graph

Graph of first person's sound wave collected in 0.03s.

a.       Yes, it is a periodic wave because there is a distinct, repeating pattern.

b.       There are about 5 waves shown in this sample. This can be measured by counting how many peaks there are.

c.       The probe collected this data in 0.03 second, which is about the time it takes for a bee to flap its wings six times.

d.      The period can be calculated from the time between one peak to the other. T = 0.0105s - 0.0036s = 0.0079s

e.       Frequency is the inverse of period. f = 1/T = 126.6Hz

f.       λ = v/f = 2.69m. This length is about the height of the classroom

g.       The amplitude is the vertical distance between the peak and the crest divided by 2. A = 0.384.

h.      If the sample were 10times as long, there will be more waves. Amplitude may change depending on how loud or soft the sound is. The wave will still be periodic. The period and frequency would stay the same, therefore the wavelength would stay the same.

Graph of first person's sound wave collected in 0.3s.

2. Second sound wave graph

Graph of second person's sound wave collected in 0.03s

a.       There are about 6.5 waves shown in this sample.

b.      T = 0.0099s - 0.0052s = 0.0047s

c.       f = 1/T = 213Hz

d.      λ = v/f = 1.61m. This length is about the height of the classroom

e.       A = 0.1945.

f.       The second wave has smaller amplitude, shorter period, and shorter wavelength compared to wave #1

3. Third sound wave graph

Graph of the tuning fork's sound wave collected in 0.03s.

The data collected from the tuning fork is a lot more sinusoidal compared to human's voice. The graph of human's sound wave looks like a superposition of multiple sinusoidal waves.

4. Fourth sound wave graph

Graph of tuning fork's softer sound wave collected in 0.03s

As predicted, compared to the third graph, the wave collected from hitting the tuning fork softer only lowers the amplitude. The wavelength and frequency of the wave stay the same.

Summary:

Regular sound that we hear daily is generally not a simple, single sinusoidal wave. Instead it looks more like a superposition of multiple sinusoidal waves. The characteristics of the wave affect the sound. Higher amplitude gives louder sound and higher frequency gives higher pitch.

Experiment 4: Standing Waves

       The purpose of this lab is to observe and analyze standing waves on a string that is under a tension and driven by an oscillator.

Experiment:

The experiment is set up as shown below

One end of the string is attached to a hanging mass and the other end
is attached to an oscillator connected to a frequency generator.

To create a standing wave, we can adjust the frequency generator.

Data and Analysis:

Length of string	1.954 ± 0.02 m
Mass of string	0.00206 ± 0.00001 kg
Linear density	0.001054 ± 1.55E-5 kg/m

1, 2, and 3.
Case 1

Harmonics (n-value)	Frequency (Hz)	# of Nodes	Distance between nodes (m)	Wavelength (m)
1	15 ±2.5	2	1.522 ± 0.01	3.044 ± 0.01
2	30 ± 2.5	3	0.761 ± 0.01	1.522 ± 0.01
3	43 ± 2.5	4	0.507 ± 0.01	1.015 ± 0.01
4	61 ± 2.5	5	0.381 ± 0.01	0.761 ± 0.01
5	73.4 ± 0.1	6	0.304 ± 0.01	0.609 ± 0.01
6	87.9 ± 0.1	7	0.254 ± 0.01	0.507 ± 0.01
7	102.9 ± 0.1	8	0.217 ± 0.01	0.435 ± 0.01
8	117.2 ± 0.1	9	0.190 ± 0.01	0.381 ± 0.01
9	131.6 ± 0.1	10	0.169 ± 0.01	0.338 ± 0.01
10	146.5 ± 0.1	11	0.152 ± 0.01	0.304 ± 0.01

Calculated speed: 43.14 ± 0.86 m/s
Speed from graph: 44.39 ± 0.2982 m/s

Case 2

Harmonics (n)	Frequency (Hz)	#of Nodes	Distance between nodes (m)	Wavelength (m)
1	7.4 ± 0.1	2	1.522 ± 0.01	3.044 ± 0.01
2	15.0 ± 0.1	3	0.761 ± 0.01	1.522 ± 0.01
3	23.0 ± 0.1	4	0.507 ± 0.01	1.015 ± 0.01
4	30.3 ± 0.1	5	0.381 ± 0.01	0.761 ± 0.01
5	36.9 ± 0.1	6	0.304 ± 0.01	0.609 ± 0.01
6	45.5 ± 0.1	7	0.254 ± 0.01	0.507 ± 0.01

Calculated speed: 21.55 ± 1.25 m/s
Speed from graph: 22.92 ± 0.3424 m/s

4. Ratio of wave speeds for case 1 compared to case 2 is 1.94. This ratio is really close to the predicted wave speed which is 2.

5. Case 1

Harmonics	Frequency (Hz)	n*f1 (Hz)	% Difference
1	15	15	0.00%
2	30	30	0.00%
3	43	45	4.44%
4	61	60	1.67%
5	73.4	75	2.13%
6	87.9	90	2.33%
7	102.9	105	2.00%
8	117.2	120	2.33%
9	131.6	135	2.52%
10	146.5	150	2.33%

The table above shows that the measure frequencies for case 1 is close to nf1

6.

Harmonics	Case 1 Frequency	Case 2 Frequency	F1/F2
1	15	7.4	2.0
2	30	15	2.0
3	43	23	1.9
4	61	30.3	2.0
5	73.4	36.9	2.0
6	87.9	45.5	1.9

The ratio of the frequency of the harmonics for case 1 and case 2 is 2, which is also the ratio between the speed of the wave for case and case 2.

Some sources of error that may affect the results of this experiment are:

- Error contributed to equipment and measuring tools such as ruler and balance

- Error contributed to the first frequency generator we used which is not digital and has a large increments.