Can a special-purpose instrument, such as an oscilloscope or a spectrum analyzer, be replaced by a general purpose computer? What features of the instrument would the computer need to accomplish this? It would need a way to acquire a signal (an input). It would need a way to process and represent the signal as selected by the user. It would need a way to display the result. The computer has these features. It has a sound card that can input signals. It has a memory and arithmetic capability that can follow a program. It has a monitor screen for display. Computer programs that emulate the functions of special-purpose instruments are generically known as virtual instruments. It is usual for the display to simulate the screen of the real special-purpose instrument. The display also depicts the knobs, pushbuttons, dials, and indicators that are typical of the real instrumentation. The user manipulates these controls with a mouse. Good virtual instrumentation can rival the quality and ease of use found in real instrumentation. An advantage of the real instrumentation is that real instrumentation is often used to measure signals that have been generated by a computer. The real instruments offer an independent confirmation.
Exercises
Exercise 1, The telephone
How many acoustical transducers are in a telephone handset? What are they?
Exercise 2, Fooling the frequency counter
On the graph in Fig.4.8draw a periodic signal that has two positive-going zero crossings per cycle. Explain why a frequency counter would display a frequency that is two times larger than the fundamental frequency of the signal. (A factor of two in frequency is called an “octave.”)
Exercise 3, All things come to him who waits.
A frequency counter displays a frequency as an integer number of cycles per second because it counts discrete events. For instance, it might display 262 Hz.
Suppose you wanted better accuracy. Suppose you wanted to know that the frequency was really 262.3 Hz. What could you do?
Exercises 37
Fig. 4.8 Your signal to fool the counter with two positive-going zero crossings per cycle
Exercise 4, Make a list
Microphones and loudspeakers are transducers. Name some other transducers.
Exercise 5, Setting the sweep rate
Suppose you want to display two cycles of a 500-Hz sine tone on an oscilloscope.
What should you chose for the period of the sawtooth sweep on the horizontal axis?
Exercise 6, The dual-trace oscilloscope
What is so important about a dual-trace oscilloscope? In what way does it have more than twice the capability of a single-trace ’scope?
Exercise 7, Oscilloscope deflection
Recall that like charges repel and opposite charges attract. The analog oscillo- scope deflects the electron beam horizontally using charged plates on the right and left side of the CRT. If you want to deflect an electron (negative charge) to the left side of the oscilloscope screen, which plate would be positively charged, and which plate would be negatively charged?
Exercise 8, Reading the frequency from the oscilloscope
The oscilloscope has ten divisions in the horizontal direction. You observe that the sweep rate control is set to “0.5 ms/div.” (Translation: 0.5 ms per horizontal division on the screen.) You see exactly four cycles of a sine tone on the screen.
What is the frequency of the tone?
Exercise 9, Estimating the frequency
The oscilloscope is set up as in Exercise 8. You observe that a single cycle of the tone covers slightly more than 2 divisions. Estimate the frequency of the tone.
Exercise 10, Spectrum analyzer and oscilloscope
A signal is sent to both the spectrum analyzer and the oscilloscope. The spectrum analyzer display looks like Fig.4.9. Explain why the oscilloscope tracing looks like Fig.4.10.
38 4 Instrumentation
Fig. 4.9 Signal for Exercise 10 on the spectrum analyzer
Fig. 4.10 Signal for Exercise 10 on the oscilloscope
Exercise 11, Oscilloscope grid
The oscilloscope grid in Fig. 4.10 has divisions spaced by 1 cm. How many volts per centimeter on the vertical scale? How many seconds per centimeter on the horizontal scale?
Chapter 5
Sound Waves
Recall that the first step in an acoustical event is a vibration of some kind and the second step is the propagation of that vibration. The opening chapters of this book introduced vibrations. Now it is time to look at that second step. Vibrations are propagated by means of sound waves. Therefore, this propagation raises the topic of waves themselves. As you know, there are many different kinds of waves—
radio waves, light waves, X-rays, and waves on the surface of a lake. Sound waves are another important example. The different waves have some common features.
They all have some frequency (or frequencies). They all can be characterized by a direction of propagation and a speed of propagation, though the speeds are different for different kinds of waves.
In general terms, a wave can be thought of as a physical means of propagating energy, momentum, and information without transporting mass. If a friend throws a ball to you, energy and momentum are propagated, and so is the mass of the ball. By contrast, if a friend subjects you to a booming bass sound, energy and momentum are again propagated (your chest walls may be temporarily deformed) but no mass is propagated. The sound comes to you as a wave. If a friend sends you a letter, you get the information and the mass of the letter. By contrast, if a friend contacts you by cell phone, you get information but no mass. The information is propagated by a radio wave.
We are particularly interested in sound waves. Sound waves can travel through solids, liquids, and gasses. What is normally most important for us as listeners is the propagation of sound waves in air (Fig.5.1).
To begin the study of sound waves in air, we start with a brief detour into the water. When you dive down into the water you feel a pressure on your eardrums.
That is because of the weight of the water on top of you. The weight of the water is due to the earth’s gravity, and this weight leads to pressure.
When you are on the surface of the earth, you are under a sea of air. Because of gravity, the air has weight and leads to pressure. It is known as standard atmospheric pressure. A pressure has units of a force per unit area. In the metric system of units, force is measured in Newtons and area is measured in square meters, and so pressure W.M. Hartmann, Principles of Musical Acoustics, Undergraduate Lecture Notes
in Physics, DOI 10.1007/978-1-4614-6786-1 5,
© Springer Science+Business Media New York 2013
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40 5 Sound Waves
Fig. 5.1 You live under a sea of air, which creates atmospheric pressure (you may have noticed that this figure is not to scale
is measured in units of Newtons per square meter, otherwise known as Pascals. One Pascal (Pa) is equal to a pressure of 1 N/m2.
Atmospheric pressure is about105or 100,000 Pa. That looks like a rather large number. There are three reasons that it looks large. The first reason is that a square meter is a large surface area. (Atmospheric pressure is only 10 N per square centimeter.) A second reason is that a Newton is not really very heavy—1/4 pound.
But the most important reason that atmospheric pressure looks large is that it really is large. Atmospheric pressure is equivalent to 14.7 pounds per square inch. To make that meaningful, understand that this means 14.7 pounds of force on every square inch of your body. Wow! You experience that pressure all the time. . . not just on Mondays. The only reason that you are not squashed by that pressure is that your insides are pressurized too. Your entire vascular system is pressurized equivalently, and you are unaware of the great weight that is upon you. You gain a little insight into this matter when you go up in an airplane or an elevator where there is slightly less atmosphere above you and consequently less air pressure. Your ears may “pop.”
A sound wave is a small disturbance in the air pressure. Where a sound wave has a peak, the air pressure is slightly greater than atmospheric pressure. Where a sound wave has a valley, the air pressure is slightly less than atmospheric pressure. The change in air pressure caused by a sound wave is very tiny.
Look at Fig.5.2. Those huge numbers on the vertical axis show pressure in Pascals. Standard atmospheric pressure is 101,325 Pa. The sound wave makes positive and negative excursions around this value. Its amplitude is only 28 Pa.
Probably you are thinking that this does not look like much of a wave. Its amplitude is less than 3 one-hundredths of a percent of the atmospheric pressure. In fact, however, this wave is huge. It is a 120-dB sine tone, and it is so intense that it