Determination of the speed of sound

background [prelab assignment (15 points) due at the begining of lab]

1. what is a "frequency spectrum" (of a sound source) ? how is it related to a FFT (fast Fourier transform) analysis (of a sound source) ?

2. what's the relationship between the frequency (of sound), the speed of sound, and the length of a column of air in a tube (with one open end and a closed end) ? based on the preceding relationship, describe how to determine the speed of sound using graphical analysis.

3. what's "aliasing" ? what's the "Nyquist frequency" ? how are the preceding two concepts related to each other ?

purpose

determine the speed of sound based on graphical analysis

use Vernier probeware's FFT feature to determine the frequency of sound (both input & output)

determine the accurary of FFT

materials

sound frequency generator [requires Mathematica or cdf player plugin]: double (?) or single  -- to test FFT feature

Vernier microphone / Logger Pro software

100 mL graduated cylinder; water; ruler

input: you ("blow") and / or tuning fork

methods / data analysis

Vernier probeware

to access data collection parameters @ Logger Pro (software):  Experiment -> Data Collection ...

student design, e.g.  you'll have to adjust the data collection parameters.  to ensure seeing the raw signal, select sample duration ~ 1.0 second & appropriate sampling rate (hint: see prelab about Nyquist frequency)

to access FFT @ LoggerPro (software):  Insert -> Additional Graphs -> FFT Graph; resize / relocate FFT & pressure vs.  time graphs accordingly

content of lab report [45 points]

Analysis using Vernier probeware [25 points]

sound with a single frequency versus two frequencies; use "beats" simulation

figure 1. signal in the time domain

figure 2. signal in the frequency domain; i.e. FFT results

using CER, compare frequency from sound source versus microphone / analyzer

analysis of "blowing" (with your mouth); include / label both time domain data & FFT results

analysis of sound by blowing over a gradulated cylinder as a function of the lenght of the air column; summarize in a data table; include / label both time domain data & FFT results

graphical analysis to determine the speed of sound and its rationale (5 points)

qualitatively, evalute its accuracy and precision; support your evaluation based on the % error. (5 points)

resources

FFT & sound (skim only)

Claims Evidence Reasoning (CER) - website

related JCE article