Download Ph331, Winter 2015 – Comprehensive Study Guide for the final

Ph331, Winter 2015 – Comprehensive Study Guide for the final exam.
This Study Guide consists of two parts: Part One has already been posted before the midterm, and
Part Two covers “after-the-midterm” topics.
PART ONE:
Simple harmonic motion (SHM), definition.
Frequency and period in SHM, the relation between the two. The displacement and amplitude. The
mathematical equation describing the time dependence of the displacement y(t) in terms of the amplitude
and frequency (you don’t need to memorize the formula, but be sure that you can identify it on a formula
sheet – a formula sheet will be provided at the test – and that you know how to use it. From now on, all
other formulas or equations you should be able “to recognize and to use” will be marked with a *
symbol).
Hooke’s Law; definition of linear restoring force; the spring constant k. The relation* between force,
spring constant, and the displacement.
Frequency and period in a simple harmonic oscillator (SHO) made of a spring with spring constant k with
a mass m attached – the mathematical formula*.
Damped harmonic oscillator – how damping affects the amplitude and the frequency? Only qualitative
description, no math.
Driven HO and resonance. The definition of resonance. Under what conditions does resonance occur?
Wave motion, travelling waves. What is travelling, and what does not travel in a travelling wave? Type s
of waves – longitudinal and transverse. Polarization. Which type of wave can be polarized? Can sound
waves be polarized?
The equation* describing a travelling wave. The parameters in the wave equation: wavelength, frequency,
phase angle, amplitude. Definition of the wavelength. The wave velocity. The relation between the
wavelength, frequency, and the wave velocity (“Dr. Tom’s Triangle”) or between the wavelength, wave
velocity and oscillation period (“Dr. Tom’s Triangle of the Second Kind”). The direction in which a
wave travels: looking at the wave equation, how can you tell whether the wave is travelling from the left
to the right, or from the right to the left?
The phase shift between two waves. The meaning of the terms “in phase” and “out of phase”.
Speed of sound in air, its dependence on temperature*. Keep in mind that that the temperature may be
expressed in the Fahrenheit scale or in Celsius scale, and they are not the same scales!
Interference: the principle of superposition. Constructive and destructive interference – relation to the
phase angles of the interfering waves.
“Beats”: when do they occur? The frequency of beats*. How many “beats” per second there are if the
frequencies of the two waves are f1 and f2 ?
Doppler Effect: the definition. The circumstances under which the Doppler Effect occurs. The motion of
the sound source, and of the observer. The equation* for the Doppler-shifted sound frequency heard by an
observer. Be sure that you know the rule how to use the “plus” and “minus” signs in the equation!
Standing waves, in general: conditions necessary to produce standing waves. Nodes and antinodes.
Standing waves produced by interference of an “impinging” and and a “backreflected” wave on a rope:
what is the pattern of nodes and antinodes in the case of: (a) a “fixed” rope end, and (b) a “loose” end?
The wave velocity V in a stretched string: the equation* relating V, the force of tension applied to the
string, and the mass of unit length of the string.
The standing waves on a tensioned string (e.g., a rope with both ends “fixed”): the fundamental
frequency of the standing wave in a string of length L. What is the wavelength for the fundamental
frequency? The frequencies and the wavelengths in the “higher harmonics”. The number of nodes and
antinodes for the n-th harmonic frequency (when considering the two fixed ends as nodes). Te equation*
for the fundamental frequency f1 in a string of length L, of mass of unit length W, and with a force of
tension F applied to it (the “Mersenne’s Law”). Be sure that you know how to use the “Mersenne’s Law”
for calculating the frequency fn of the n-th harmonic.
Methods of exciting standing waves in strings in various types of string instruments (bowing, plucking).
Standing waves in air columns. The waves that may form in tubes with (a) two open ends, (b) one open
end and one closed end, and (c) two closed ends. The wavelengths for the fundamental frequency and the
higher harmonic frequencies, and the positions of nodes and antinodes in each case. Possible harmonic
frequencies: for which tubes all n-s are possible, and for which only odd n values may occur? “Adjacent
frequencies”: if a tube has an open end, and it has two “resonant” frequencies fA and fB, and surely there is
no resonant frequency in between, how can you find out what is the fundamental frequency for this tube,
and whether the other end is “open”, or ‘closed”?
PART TWO
(note: I’m writing down what comes to my mind right now, late in the evening on Thursday, March
12. But if something else comes to my mind later, I will add it – and use a different font color to
indicate that such an item is a “later addition”. So, please check more than once what is written in
this study guide – and observe your e-mail. If I make some “relevant” additions, I will not only
show them by a different color, but I will alos send an e-mail to all of you).
Woodwind and brass instruments. Is a woodwind instrument necessarily made of wood? What is the
criterion for the instrument for being classified as a “woodwind” or a “brass”?
Renaissance instruments, “cornetto” and “serpent”. Modern brass instruments: you don’t need to konow
all details, but, at least, you should be able to tell the difference between, say, a tuba and a trombone.
The spectrum of a sound. Harmonic analysis, the Fourier components of a sound.
The sound waveform: the “ADSR envelope”. What does each letter stand for? What part of the ADSR
envelope plays a crucial role in the recognition of the sound source?
Sound recording: analog and digital methods. Basic facts from the history of sound recording. Who
produced the first ever record of human voice? Edison’s “phonograph” – how did it work? Two
competitive techniques: recording on a cylinder and on a disc. Why did the latter eventually win –
eventually? Magnetic analog recording: brief history.
(the analog techniques of sound recording are now obsolete, or “almost obsolete”, i.e., only a small
community of hobbyists and hi-fi geeks are still fond of them. However, sound recording and the progress
in various recording techniques had a profound impact on the XXth Century culture, and still has much
impact on today’s popular culture: for instance, if the progress in sound recording techniques was slower,
nobody today would know about the four British youngsters who at the beginning of 1960-ties formed
“The Beatles” band).
Sorry, this paragraph got here by mistake – disregard it; it’s from the last year’s guide, but this year we
did not talk about digital recording. Digital recording of sound. Binary numbers, binary and decimal
representations of numbers. Converting decimal numbers to binary representation: a simple method, by
consecutive divisions by 2 and writing down the remainders from each division from the right to the left
(we did that in class). How is the sound signal “digitized”? The frequency of the sampling: how often
should the “elementary probing operations” be done to assure the high quality of the recorded music –
what does the “Nyquist Theorem” say? What is the internationally accepted standard for the sampling
frequency for music to be stored on compact discs? And how are the results of sampling stored in CDs?
Modern devices for sound recording, and for the reproduction of electronically recorded music. The
dynamic microphone and the dynamic loudspeaker. The Faraday Law of electromagnetic induction and
its application in dynamic microphones. The Lorenz Force acting on a wire with current in a magnetic
field, and how it is taken advantage of in the loudspeakers (you don’t need to know the mathematical
formulas associated with the Faraday Law and the Lorentz Force, a “conceptual understanding” is OK).
The similarities in the microphone and loudspeaker design: can a loudspeaker act as a microphone? And a
microphone, as a loudspeaker? (FYI: a high quality dynamic microphone could be nothing more than a
“whisperer”, but definitely not a LOUDspeaker).
Human ear: you need to be able to name the main parts and components, such as the tympanic
membrane, the tiny boned in the middle ear and their role, and the essential organ in the inner ear, which
transform the sound vibrations to nerve pulses which are then processed by the brain – but you don’t need
to know the details of transformation process itself (there is some explanation of the transformation
mechanism in the book, but there won’t be questions about it in the exam).
Sound intensity. The pressure amplitude and the power carried by a sound wave. The units {Newtons per
square meter, Watts per square meter). The lowest intensity the human ear can recors, and the highest
intensity we are able to withstand without pain – what is the ratio of the two? Why we choose to use a
logarithmic scale rather than a linear scale to express the sound intensity? What are the units in the log
scale (Bel and deciBel). What is the “SIL”? Be sure you understand the basic formula for calculating the
SIL (if you understand the example we did in class, with the 76 trombones, you are OK).
Musical temperament. Bascic notions, such as the frequency intervals, octave, diatonic scale, and the
twelve-tone equal temperament (“12-tET”, the principal standard in Western music for more than 200
years). Pythagorean scale -- be sure you know how it is “built up”, using the “perfect fifths”, and
shifting them down or up by an octave or two, if they don’t fall into the octave defined by the
“fundamental tone” (it is all explained in the Youtube movie, the link to which is given in the course
Web page). The modern twelve-tone equal-temperament scale: What is the frequency ratio of two
adjacent tones in the 12-tET system? Be sure that you can also calculate the ratio of the frequencies of
two tones that are two positions apart in the scale, three positions apart, etc.