|1 ||Light travels faster in warmer air. Use this fact to explain the formation
of a mirage appearing like the shiny surface of a pool of water when there
is a layer of hot air above a road.
|2 ||(a) Using the equations from optional section 4.2, compute the amplitude
of light that is reflected back into air at an air-water interface, relative
to the amplitude of the incident wave. The speeds of light in air and water
are 3.0x108 and 2.2x108 m/s, respectively.
(b) Find the energy of the reflected wave as a fraction of the incident
energy. [Hint: The answers to the two parts are not the same.]
|3 ||A B-flat clarinet (the most common kind) produces its lowest note, at
about 230 Hz, when half of a wavelength fits inside its tube. Compute
the length of the clarinet. [Check: The actual length of a clarinet is about
67 cm from the tip of the mouthpiece to the end of the bell. Because the
behavior of the clarinet and its coupling to air outside it is a little more
complex than that of a simple tube enclosing a cylindrical air column,
your answer will be close to this value, but not exactly equal to it.]
|4 ||(a) A good tenor saxophone player can play all of the following notes
without changing her fingering, simply by altering the tightness of her
lips: Eb (150 Hz), Eb (300 Hz), Bb (450 Hz), and Eb (600 Hz). How is
this possible? (b) Some saxophone players are known for their ability to
use this technique to play "freak notes," i.e. notes above the normal range
of the instrument. Why isn't it possible to play notes below the normal
range using this technique?
The table gives the frequencies of the notes that make up the key of F
major, starting from middle C and going up through all seven notes. (a)
Calculate the first five or six harmonics of C and G, and determine
whether these two notes will be consonant or dissonant. (b) Do the same
for C and B flat. [Hint: Remember that harmonics that differ by about 1-
10% cause dissonance.]
|6 ||Brass and wind instruments go up in pitch as the musician warms up.
Suppose a particular trumpet's frequency goes up by 1.2%. Let's consider
possible physical reasons for the change in pitch.
(a) Solids generally
expand with increasing temperature, because the stronger random motion
of the atoms tends to bump them apart. Brass expands by 1.88x10 -5 per
degree C. Would this tend to raise the pitch, or lower it? Estimate the size
of the effect in comparison with the observed change in frequency.
speed of sound in a gas is proportional to the square root of the absolute
temperature, where zero absolute temperature is -273 degrees C. As in
part a, analyze the size and direction of the effect.
(c) Determine the
change in temperature, in units of degrees C, that would account for the
|7 ||Your exhaled breath contains about 4.5% carbon dioxide, and is
therefore more dense than fresh air by about 2.3%. By analogy with the
treatment of waves on a string in section 3.2, we expect that the speed of
sound will be inversely proportional to the square root of the density of
the gas. Calculate the effect on the frequency produced by a wind instrument.||