Ph331, Winter 2017 – Study Guide for the midterm exam.
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”?
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”?
Pure tones (perfect sine waves) and “real” tones: their components – the “fundamental tone” and the
“harmonics”. The Fourier spectrum of a real tone, showing the the amplitude of the harmonic tones in a
given sound wave. Fourier synthesis and analysis.
The “asterisk” symbol * means that the mathematical formula marked by it will be listed in the “formula
sheet” you’ll get at the exam. Accordingly, you don’t need to memorize the mathematical formulae we
have discusses in class – but you have to be able to recognize the formulae and the constituent symbols in
each of them. For instance, you should be able to tell that the following equation:
𝜔 = 2𝜋𝑓 = √
𝑘
𝑚
describes the oscillation frequency of a spring oscillator, and you should know what is the meaning of
each symbol (ω, f, k and m) in this equation.