Question

Lab 12. Sound Waves and Beats Introduction Sound waves consist of a series of air pressure variations. A Microphone diaphragm records these variations by moving in response to the pressure changes. The diaphragm motion is then converted to an electrical signal. Using a Microphone and an interface, you can explore the properties of common sounds. The first property you will measure is the period, or the time for one complete cycle of repetition. Since period is a time measurement, it is usually written as T. The reciprocal of the period (1/T) is called the frequency, f, the number of complete cycles per second. Frequency is measured in hertz (Hz). 1 Hz=15 WA second property of sound is the amplitude. As the pressure varies, it goes above and below the average pressure in the room. The maximum variation above or below the average pressure is called the amplitude. The amplitude of a sound is closely related to its loudness. In analyzing your data, you will see how well a sine function model fits the data. The pressure in the medium carrying a periodic wave can be modeled with a sinusoidal function. Your textbook may have an expression resembling this one: y= Asin (276ft) In the case of sound, which is a longitudinal wave, y refers to the variation in air pressure as a function of time, t(See Fig. 1). A is the amplitude of the wave and fis the frequency. The factor of 24 ensures that when t = T, the sine function will have gone through one complete cycle. When two sound waves overlap, air pressure variations will combine. For sound waves, this combination is additive. We say that sound follows the principle of linear superposition. Beats are an example of superposition. Two sounds of nearly the same frequency will create a distinctive, cycling variation of sound amplitude, which we call beats. Objectives Measure the frequency and period of sound waves from a tuning fork. Measure the amplitude of sound waves from a tuning fork. Observe beats between the sounds of two tuning forks. Task: Complete the tables Analysis Part 1: #2&3 2, Since the model parameter B corresponds to 29(i.e., f=B/(20, use your fitted model to determine the frequency. Enter the value in your data table. Compare this frequency to the frequency calculated earlier. Which would you expect to be more accurate? Why? 3. Compare the parameter A to the amplitude of the waveform.
Please help with question 2,3 and 4 and filling out the table

Answer 1

1. Below is the completed filled data table

Part 1	Simple	Waveforms
Tuning Fork Frequency	Number of Cycles	del(t) s	Period (s)	Calculated Frequency (Hz)	% error
512	25	0.0475	0.0019	526.3157895	2.796053
480	29	0.0609	0.0021	476.1904762	-0.79365
Tuning Fork Frequency	Amplitude
512	0.4534
480	0.09782
Tuning Fork Frequency	Parameter A	Param B	Param C	Param D	f = B/2*pi
512	0.4534	3221	1.519	0.001272	512.6381	0.124623
480	0.09782	3010	3.952	0.001679	479.0564	-0.19659

From the data table we can see,
2. calculated frequency in table 1 has more error as compared to frequency calculated from parameter B
hence frequency calculated through method 2 is more accurate
this is because method 2 is graph based, which takes average of many observations and hence thats why calculations from table 2 are more accurate

3. From table 2, and 3
we say parameter A and amplitude is exactly the same for both the tuning forks

4. For the beats the table is as under

Cycles	del(t) s	Period (s)	Frequency (Hz)
10	0.03	0.03	33.33333

From the table, beat frequency from calculations is 33.33 Hz,
from theory the beat frequency should be 512 - 480 = 32 Hz
hence calculated beat frequency is close to theoretical beat frequency