Lab 5: Introduction to Sound (5) s

Purpose:

In this lab we will examine the periodic nature of sound waves by analyzing sound of human voice and tuning forks.



Method:

We will be using logger pro and an attach microphone to obtain a graph of sound pressure vs. time to analyze the nature of sound waves.

Figure 1: Microphone recording sound wave from tuning fork.

Data and Analysis:

Figure 2: Sound Pressure vs. Time (human) 

• Sound wave is periodic as evidence by the sinusoidal behavior of the graph.
• There are 7 waves in the data collected in Figure 2, we designate the gap between two crest to be one wave.
• The time frame in Figure 2 is comparable to a flash of eye.
• T = 0.0038 ± 0.0001 s, the period is define by the time it takes to complete one cycle.
• ƒ = 262 ± 7.59 Hz,  ƒ  = 1/ T  
• λ = 1.30 ± 0.039 m,  λ = v / f, the length is comparable to a meter stick.
• Amplitude A = 2.718 ± 0.2 W, we took the average of the two different peak to determine the amplitude of the wave. 

Figure 3: Sound Pressure vs. Time (human, t = 0.3)

• All characteristic of Figure 3 will be similar to Figure 2 except the time frame will be ten times as long.

Figure 4: Sound Pressure vs. Time (human) 

• There are 3 waves in Figure 4.
• ƒ = 129 ± 5.81 Hz
• T = 0.01132 ± 0.002 s 
• λ = 2.63 ± 0.057 m
• A = 0.14 ± 0.02 m
• The sound wave in Figure 4 has a lower frequency and smaller amplitude than that of Figure 2.

Figure 5: Sound Pressure vs. Time (tuning fork) 

• The graph made by tuning fork is much smoother due its ability to produce sound waves in a single set of frequency. 

Figure 6: Sound Pressure vs. Time (tuning fork)

• The loudness of a frequency is determined by the amplitude of the wave, thus Figure 6 has a lower amplitude than Figure 5.

Conclusion:

In this lab we have analyze the property of the sound wave graphically. We find that sound waves are generally periodic as shown in the repetitive pattern. And the intensity and loudness of sound is directly proportional to the amplitude of the wave. We also discover that single frequency sound wave act as a sinusoidal wave. This proves that human voice does not produce one frequency but multiple while talking.  

Lab 4: Standing Waves (4) x

Purpose:

In this lab we will examine the properties and characteristics of a standing waves driven by external force.


Method:

Trials	Node	d Between node	F	W
1	2	204+/- 0.01 cm	10.6+/-0.01 Hz	408+/- 0.01 cm
2	3	102+/- 0.01 cm	19.2 +/-0.01 Hz	204+/- 0.01 cm
3	4	73+/- 0.01 cm	29.66 +/-0.01 Hz	146+/- 0.01 cm
4	5	52+/- 0.01 cm	42.59 +/-0.01 Hz	106+/- 0.01 cm
5	6	43+/- 0.01 cm	51.5 +/-0.01 Hz	84+/- 0.01 cm
6	7	37+/- 0.01 cm	60.8+/-0.01 Hz	74+/- 0.01 cm
7	8	30+/- 0.01 cm	71.9 +/-0.01 Hz	60+/- 0.01 cm
8	9	25+/- 0.01 cm	83.04 +/-0.01 Hz	50+/- 0.01 cm

Wave Speed

Case 2

Trial	Node	d between node	F	W
1	2	93.25+/- 0.01 cm	11.9+/-0.01 Hz	186.5+/- 0.01 cm
2	3	62.2+/- 0.01 cm	16.25 +/-0.01 Hz	124.4+/- 0.01 cm
3	4	46.6+/- 0.01 cm	21.77+/-0.01 Hz	93.2+/- 0.01 cm
4	5	37.3+/- 0.01 cm	27.97 +/-0.01 Hz	74.6+/- 0.01 cm
5	6	31+/- 0.01 cm	33.77 +/-0.01 Hz	62+/- 0.01 cm
6	7	26.6+/- 0.01 cm	39.83+/-0.01 Hz	53.2+/- 0.01 cm
7	8	23.3+/- 0.01 cm	45.73 +/-0.01 Hz	46.6+/- 0.01 cm
8	9	20.7+/- 0.01 cm	51.23 +/-0.01 Hz	41.4+/- 0.01 cm

Conclusion:

Due to the linear relationship between frequency and wavelength, we have validate the frequency wavelength equation. The velocity of the oscillating wave corresponds to the slope of the trendlines. The two graph have similar velocity thus we conclude that the equation is valid.

Lab 3: Speed of Transverse Wave s

Purpose:

In this lab we will determine the frequency and wavelength of an oscillating spring and validate the equation:  v = λƒ

Method:

To attain our objective, we will be recording three sets of data from three oscillating spring with distinct wavelengths. The period and frequency of the three sets of waves will be measured and a graph of frequency vs. wavelength will be plotted to validate the inverse relationship between  λ and ƒ.

Figure 1: Oscillating spring.

Data and Analysis:

Figure 2: Recorded period of the waves.

Table 1: Wavelength, time, period, frequency and velocity of the three sets of oscillating spring.

λ(m)	t (s)	T (s)	ƒ (Hz)	v (m/s)
6.0 ± 0.01	9.30 ± 0.1	0.930 ± 0.001	1.08 ± 0.006	6.48 ± 0.047
3.0 ± 0.01	4.40 ± 0.1	0.440 ± 0.001	2.27 ± 0.002	6.81 ± 0.029
2.0 ± 0.01	2.56 ± 0.1	0.256 ± 0.001	3.91 ± 0.019	7.82 ± 0.077

Figure 3: Equation in this lab.

Figure 4: Frequency vs. Wavelength plot

• The above graph validates the equation  v = λƒ by showing the inverse relationship between wavelength and frequency through the inverse trend line.

Table 2: Relationship of frequency wavelength graph.

Theoretical Power of x	Experimental Power of x	Percent Error (%)
-1	-1.16	16

Conclusion:

In this lab we have examine the validity of the frequency wavelength equation by analyzing the wave properties of an oscillating spring. We find that the frequency and wavelength exhibits an inverse relationship that corresponds to the equation. Although the relation shows a 16% error we find that this is acceptable due to the minimal set of points available to fit the trend line. We also think that the measurement of time can be more precise to increase the accuracy of the graph. In addition we have also determine the uncertainty of the calculations by determining the range between the maximum and minimum value.