Guitar String Lab

Goal: 
To investigate the guitar and its frequencies.

Materials:

Microphone with computer

Guitar

Meter stick

Background:

• Fundamental frequency: The lowest frequency present in the sound spectrum.

• Sound spectrum/ FFT graph: A graph of the frequencies present in a sound wave.

Process:

Part 1 we measured the Hz of an open string on Logger Pro and looked for the lowest frequency. Then we measured the frequency of every fret until we found a frequency that was twice the original.

Part 2 we measured the actual lengths of the strings with a ruler

Part 3 To match two strings, we chose the middle two, G and D. We found that if we held the 5th fret of the D string that they matched.

Data:

  For this lab, we used the the low E string

Open	88
1st  Fret	92
2nd Fret	100
3rd Fret	105
4th Fret	110
5th Fret	117
6th Fret	124
7th Fret	130
8th Fret	140
9th Fret	147
10th Fret	154
11th Fret	166
12th Fret	180

To match two strings, we chose the middle two, G and D. We found that if we held the 5^th fret of the D string that they matched.

String Lengths

Open	64.5cm
1st  Fret	60.7cm
2nd Fret	57.4cm
3rd Fret	54.1cm
4th Fret	54.1cm
5th Fret	48.3cm
6th Fret	45.5cm
7th Fret	43.0cm
8th Fret	40.6cm
9th Fret	38.4cm
10th Fret	36.3cm
11th Fret	34.2cm
12th Fret	32.3cm

Equation = Hz = .95/ L

Conclusion: 
In this lab we learned how guitars work to achieve different frequencies. The length of the guitar string is key in the frequency. Also we learned how changing the length will eventually lead you to the same frequency as before but of a different octave.

Sound Unit Intro Lab

Goal: 
To orient ourselves with the lab equipment and determine the experimental value of the frequencies of different tuning forks.

Background Information:
Sound waves are the vibration of air molecules that originate at a vibrating source, such as our sound box. The vibrations create high and low pressure regions that can be detected by the human ear (within a certain range). Tuning forks are unique from most sound-making objects in that they produce just one frequency while other objects like a guitar produce a combination of multiple frequencies. Two factors that impact the pitch of the sound wave are frequency and period.

Frequency = 1/Period
Period = 1/Frequency

Process: 
In this lab, we used Logger Pro to graph the sinusoidal wave of the sound wave. Using this graph, we were able to measure the period of the function. With this information, and the equations above, we determined the experimental value of the frequency of the tuning fork and compare it to the value written on the fork.

Data:

Experimental Period: 0.002654 s

Accepted Frequency (written on fork): 384 1/s

Accepted Period: 1/384 = 0.0026041667 s

Experimental Frequency: 1/0.002654 = 376.7897513 1/s

Percentage Error: 1.88% 

Experimental Period: 0.002440 s

Accepted Frequency: 426.7 1/s

Accepted Period: 0.00234357 s

Experimental Frequency: 1/0.002440 = 409.8260656 1/s

Percentage Error: 3.95%

Experimental Period: 0.007920 s

Accepted Frequency: 128 1/s

Accepted Period: 0.0035714286 s

Experimental Frequency: 1/0.007920 = 126.2626263 1/s

Percentage Error: 1.36%

Conclusion:
With this lab, we learned to use the equations that we learned in class. The lab allowed us to gain a better understanding of the relationship between period, frequency and pitch. 

Musical Scales Lab

Goal: 

To understand the mechanisms of the musical scale and find the frequencies of the notes between C and the C one octave higher. 

Background Information: 

Any note that is one full octave above another note also has twice the frequency of the lower note. Therefore, the note that is one full octave lower has half the frequency of the higher note. For example, a C that has a 100 Hz frequency has a C one octave higher than it with a 200 Hz frequency. According to the Greeks, a perfect 5th, or musical interval, can be composed by two notes that have a 3:2 ratio. 

Process: 

Since the Greeks claimed that a perfect fifth is a simple 3:2 ratio, we used this as our guide for establishing our scale. This means that we started with 100 Hz (C) and proceeded to multiply it by 1.5, and continue to multiply those results by 1.5 until the value exceeds 200 Hz. Once the value has reached or surpassed 200 Hz, we have passed the frequency value for the C one octave above the C at 100 Hz. After ordering them, we can see that this scale does not give us values of frequencies with constant ratios. Therefore, we are instructed to use a different method which will give us values of frequencies with correct ratios.
To find a more precise scale, also known as an even-tempered scale, we calculated the ratio needed to space the notes equally

Original 12 note scale:

C: 100 Hz
C#: 106.7871094 Hz
D: 112.5 Hz
D#: 126.5625 Hz
E: 142.3828125 Hz
F: 150 Hz
F#: 160.1806641
G: 168.75
G#: 189.84375 Hz
A: 213.5742188 Hz
A#: 225 Hz
B: 253.125 Hz
C: 284.765625 Hz


Even Tempered Scale:

100x^11=200
x^11=2
x= 1.059462094


C: 100 Hz
C#: 105.9463094 Hz
D: 112.2462048 Hz
D#: 118.9207114 Hz
E: 125.9921049 Hz
F: 133.4839852 Hz
F#: 141.421356 Hz
G: 149.8307074 Hz
G#: 158.7401048 Hz
A: 168.1792826 Hz
A#: 178.1797431 Hz
B: 188.7748619 Hz
C: 199.9999993 Hz

Conclusion:
This lab demonstrates to us the complex nature of musical scales and the use of ratios in creating them. Given the need for evenly spaced scales (with ratios not absolute differences), we must use exponents to find the values for our scales.

Speed of Sound Lab

Goal:
To determine an experimental value for the speed of sound.

Background Information:
The speed of sound is impacted by many different factors, including but not limited to temperature, pressure, humidity and composition of molecules in the air. The density and organization of molecules (gas, liquid or solid) influences the speed of sound.

Process:
For this lab, we used a long, thin cardboard box to determine the speed of sound. Using Logger Pro, we were able to determine the amount time it took for the sound waves of a snap to travel from the opening to the box, bounce off the other end and travel back to the opening.

Data:

Distance = speed * time
Speed = distance / time

Trial 1: ∆t = 0.0053457 s
Trial 2: ∆t = 0.0052639 s
Trial 3: ∆t = 0.0054821 s
Trial 4: ∆t = 0.0055367 s
Trial 5: ∆t = 0.0057821 s
Average value: ∆t = 0.0054821 s
Length of box: 97.5 cm
Distance travelled by sound: 195 cm / 1.95 m

Experimental speed of sound: 1.95 m / 0.0054821 s = 355.7031065 m/s
Accepted speed of sound at sea level: 340.29 m/s
Percent error: 4.53%

Conclusion:
This allowed us to find the experimental speed of sound on our own. It also allowed us to understand the variability of the speed of sound depending on many different factors. Though the accepted speed of sound at sea level is 340.29 m/s it is not entirely accurate to say that our percentage error was 4.53% given the inconsistency of the matter.

Phones Touch Tones Lab

Description of Lab:

For this lab, we recorded the noises made by each number on our phone keyboard. Using a microphone and going key by key on speakerphone, we measured the frequencies produced. Afterwards, we looked for patterns between the different frequencies and their relationship on the keyboard.

Goal of Lab:

The goal was to investigate the relationship between the frequencies made by the different keys on our phone. We looked at the frequencies of the noise made by each of the numbers on a phone keyboard, and in doing so, we found a pattern related to each key's location on the keyboard.

Data:

1: 698 and 1200
2: 700 and 1335
3: 700 and 1477
4: 760 and 1200
5: 769 and 1335
6: 760 and 850
7: 850 and 1200
8: 850 and 1335
9: 850 and 1477
*: 940 and 1200
0: 940 and 1335
#: 940 and 1477

Conclusion:

We learned that each column had an assigned frequency, as did each row. The peaks on our graph represented these two. The first peak represented the row value, and the second peak represented the column value

Standing Waves in Tubes Lab

Goal: 
To investigate the correlation between the length of a tube in water and how it resonates with different notes

Background information:

Musical instruments use pipes

The length of the pipe determines the pitch or frequency

Each length of pipe has a frequency that matches or resonates.

Materials:

Large graduated cylinder filled 7/8 with water.

PVC pipe

Meter stick

Various tuning forks

Process:

Dip the PVC pipe in the water. Then Hit the fork and hold it next to the pipe. Adjust the pipe up and down until the fork resonates. Measure this lenghth  with a ruler and write it down

Data:

A426.7: 7.5"

G384: 9.25"
E320: 10.75"
D288: 11.75

Conclusion:

We learned that the length of a pipe correlates to the frequency of a note. If the length is just right, the note resonates! This information is vital in understanding how musical instruments work.