17.3 Dynamic Range 185
186 17 Distortion and Noise
Exercises
Exercise 1, Less hum across the pond
European countries use electrical power with a frequency of 50 Hz. Do you expect that “hum” is less audible in European audio gear?
Exercise 2, Too much of a good thing
Why does nonlinear distortion occur if an amplifier is “overdriven.”
Exercise 3, Rock ‘n’ roll
(a) How does nonlinear distortion in the amplifier make chords played on an electric guitar sound “thicker?” (b) If nonlinear distortion makes music sound bad why would the rockers deliberately choose distortion?
Exercise 4, Choose a test signal
You will use your ears to evaluate an audio system for nonlinear distortion. You have a choice of signal sources to put into the system. What do you choose? (a) broadband noise? (b) a complex periodic tone with many harmonics? (c) a sine tone with frequency of 5,000 Hz? (d) a sine tone with frequency of 500 Hz?
Exercise 5, Harmonic distortion
A 1,000-Hz sine tone is put into a nonlinear device causing harmonic distortion.
What is the fundamental frequency of those harmonics?
Exercise 6, All the distortion components
You put the sum of two sine tones into a nonlinear device. The sine tone frequencies are 1,000 and 1,200 Hz. What are the frequencies of harmonic distortion products that emerge? What are the frequencies of difference tones that emerge?
What are the frequencies of summation tones that emerge? What frequencies are likely to be most audible?
Exercise 7, Worse and worse with up and down
The sine tone frequencies from Exercise 6, 1,000 and 1,200 Hz form the musical interval known as a minor third (See Appendix D if you want to know more about musical intervals.) Suppose the upper frequency is changed from 1,200 to 1,250 Hz.
The frequencies of 1,000 and 1,250 Hz make the interval of a Major third. What happens to the difference tone given by2f1f2when this change occurs?
Exercise 8, Dynamic range
An audio system produces 0.1% harmonic distortion (mostly second and third harmonics) when the level is 90 dB. The noise background is 10 dB. What is the dynamic range of this system?
Exercise 9, Audio amplifier makes toast
This chapter says that electrical power from the outlet in the wall is a 60-Hz sine wave. How is that different from a 60-Hz signal created by a computer sound card and then passed through a power amplifier? If it’s not different, why can’t you connect a toaster to the power amplifier of your stereo system? (You’d make the connection to the power amplifier just where you would normally connect the loudspeakers.)
Exercises 187
02004006008001K1.2K1.4K1.6K1.8K2K2.2K2.4K2.8K2.6K Fig.17.4Thespectrumofarecordedcarhorn.(ItwasaBuick.)Themeasuredsoundlevelwas98dB,asmeasuredwithanA-weightedsoundlevelmeter
188 17 Distortion and Noise
Exercise 10, Thinking like an acoustician—The car horn
Acousticians try to find physical explanations for human perceptions of sound qualities. The sound of a car horn is an example. The acoustician thinks that the perception can characterized by a loudness and a tone color.
1. Assuming that the spectrum is broadband, having both low and high frequencies, an intuitive approximate sense of the loudness will be gained from a decibel reading on a sound level meter. That is a single, easy measurement to make: Put a sound level meter 3 m in front of a car, blow the horn, and read the meter.
2. The tone color will be quantified by recording the sound electronically and studying its spectrum, as shown in Fig.17.4. The horizontal axis shows frequency in Hertz. The vertical axis shows the levels of the spectral components in decibels, but the scale is arbitrary. No problem. You don’t really need the absolute values of dB on the spectral plot because you already have a sense of scale from the reading you made with the sound level meter. Instead, you are concerned with the relative levels of the different components. It is typical to take the tallest peak as a reference level. Then all the other peaks have levels that are negative. In the case of the car horn, however, it makes sense to take the component at 350 Hz as a standard for the level because it is both a tall peak and a low-frequency peak.
(a) First, consider the frequencies of tall peaks in the spectrum from 0 to 2,800 Hz.
Do you see some mathematical relationships in the list of frequencies? Do you see harmonics? What does this tell you about the car horn sound?
(b) If you find more than one fundamental frequency, what does this suggest about how car horns are made or installed?
(c) If you find that there are two fundamental frequencies, determine the ratios of those frequencies. Compare with the ratios in Appendix D to determine the musical interval in the car horn sound.
(d) Can you account for all the peaks in the spectrum by assuming that they are harmonics?
(e) Can you see some distortion components? What are their frequencies and how can you account for them?
Chapter 18
Audio Systems
The purpose of this chapter is to identify some concepts and terms describing audio systems. There is a wide variety of audio systems, ranging from gigantic sound reinforcement systems for stadiums to smart phones and iPods for personal use.
Mostly, this chapter will deal with the ideas that are central to practical audio processes. The chapter begins by being amazed about the concept of sound recording.