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P105 Basic Physics of Sound
IU Physics Dept., Spring 2008
Test #2
March 24, 2008
Instructions:
- Please do not start the exam until instructed!
- Print your Name and ID# and sign your NAME at the top of this page.
- Calculators are allowed. No books or notes are allowed.
- The exam consists of 5 Questions (8 points each or 40 points) and
5 problems (12 points each or 60 points), for a total of 100 points.
Please budget your time with these values in mind.
- The last two pages contain Equations, Conversion Factors and Constants, and
Figures. You may gently tear off these last two pages for use during the test.
6. If you have any questions or if you need extra paper, please raise your hand.
7. At the end of the exam please turn in your test paper at the front of the room.
- Please keep your work covered and your eyes on your own paper during the
exam. The penalty for cheating is an automatic zero.
9. Good luck!
# Max Score
1 8
2 8
3 8
4 8
5 8
612
712
812
912
10 12
Total 100
I. Questions: 40 points (Show work & answers with units to receive full credit!)
Q1. Give the units in which the following sound parameters are expressed:
Intensity: ______
Intensity Level: ______
Loudness Level: ______
Pitch: ______
Q2. Match the pairs of physical stimulus and physiological/psychological sensation
by filling in the appropriate blank.
Stimulus Sensation
(a) ______ and Pitch
(b) Intensityand ______
(c) ______ and Timbre
Q3. What is the basilar membrane, where is it located, and what is its function?
Q4.
(a) Three pure tones with frequencies of 300 Hz, 500 Hz and 800 Hz are played together.
Is a virtual pitch heard? If so, at what frequency? If not, why not?
(b) Three pure tones with frequencies of 200 Hz, 600 Hz and 800 Hz are played together.
Is a virtual pitch heard? If so, at what frequency? If not, why not?
Q5.
The frequency spectrum (vertical lines) for a particular vowel sound spoken by a child is shown in the plot above, along with an envelope function that represents the response of the vocal tract as a function of frequency.
(a) What frequency (in Hz) corresponds to the pitch that is heard? ______
(b) What feature of human vocal system causes the vertical lines to be evenly spaced? Explain.
(c) List the formant frequency or frequencies below.
II. Problems: 60 points (Show your work to receive full credit. Answers must have units!)
P1. The amplitude of the pressure variation in a sound wave of frequency f = 200 Hz
Is measured to be 2.0 10-1 N/m2 at a distance of 2 meters from the source.
(a) What is the pressure level Lp of the sound wave (in decibels)?
(b) What is the sound intensity level LI (in decibels)?
(c) What is the loudness level, LL (in phons), of the perceived sound?
P2. A pure sound wave of frequency of 400 Hz is measured at a distance of
1 meter from the source to have an intensity level of 73 dB.
(a) What is the intensity of the sound in W/m2 at this location?
(b) What is the intensity level (in dB) of this sound at a distance of 5 meters?
(c) Suppose the sound power produced by the source is increased by a factor of 8.
What is the new intensity level (in dB) of the sound at a distance of 1 meter?
P3. A complex tone consisting of a square wave with a period of 4.00 ms can be
constructed by adding a series of pure tones with different frequencies and
amplitudes.
(a) What are the frequencies fA and fB of the two lowest-frequency pure tones in
this series?
(b) Sketch the waves (pressure versus time) corresponding to these two pure tones.
(c) What is the ratio of amplitudes AB/AA for these two tones?
P4. The frequency spectrum of the sound from a string bass shows strong contributions from the first three harmonics when a string is plucked near the bridge. Suppose two notes, the A1 (f = 55.0 Hz) and the F2 (87.3 Hz), are plucked simultaneously by two bass players.
(a) 3 pts. In principle, can beats be heard? If so, at what frequency? If not, why not?
(b) 3 pts. For the corresponding case of two violinists playing an A4 (440 Hz) and an F5 (698.6 Hz), can beats be heard? If so, at what frequency? If not, why not?
(c) 6 pts. Describe how sound is generated by string instruments like those in the violin or acoustic guitar families when a string is plucked.
P5. The lowest string of an electric guitar, E2 (82 Hz), has 25 frets or 24 fret intervals.
(a) If each fret interval corresponds to a semitone interval (frequency ratio = 1.0595),
what is the highest frequency that can be played on this string?
(b) The string has a length L = 0.65 m. What is the wavelength of the fundamental
mode of vibration of the open string?
(c) What is the velocity of transverse vibrations on this string?
(d) The tension on the string is initially 20 N. To what value must the tension be
adjusted so that the pitch of the open string is higher by two semitones?
Equation Sheet for Test #2
Equations
Energy: kinetic energy KE = (1/2)mv2; potential energy PEgrav = mgh & PEspr = (1/2)Kx2
Work and Energy: Work = Force distance; W = Fd; Work done = KE
Conservation of energy: KE + PE = constant = Etotal = (1/2)m(vbot)2 = mghtop for free fall
Periodic motion: frequency f (Hz); period T (s); f = 1/T; amplitude A; PEmax = (1/2)KA2
Mass on spring: Fsp = - Kx, f = (1/(2π))√(K/m); Pendulum: f = (1/(2π))√(g/l)
Relations involving v, the wave speed:
- wave relation: v = f
- sound wave in air: v = (331.3 + 0.6 tC) m/s -> at 20C v = 343.3 m/s
- wave on a string: v = √(T/), T is string tension [N] and is mass/length [kg/m]
Wave propagation: reflection (inc = refl); refraction (speed varies); diffraction (size~)
Wave interference: due to path length difference, (d2 – d1) or
due to frequency difference, f2f1, ffused tone = (1/2)(f2 + f1); fbeats = f2 – f1
Harmonic Series for Standing waves: harmonic number n, fundamental is n = 1
On a string: fn = nf1, n = 2L/n, fn = v/n = (n/(2L))√(T/), for n = 1,2,3…
Open air-filled pipe: fn = v/n = (n/(2L))v, for n = 1,2,3…
Closed air-filled pipe: fn = v/n = (n/(4L))v, for n = 1,3,5…
Sound: Pressure p(N/m2) and Intensity I(W/m2); I = (p2)/() (p2)/(400)
Intensity level LI (dB); LI = 10 log (I/I0), where I0 = 1.0 10-12 W/m2
Lp = 20 log (p/p0), where p0 = 2.0 10-5 N/m2
Relative level LI (dB); LI = LI2 - LI1 = 10 log (I2/I1); for I2/I1 = 2n, LI = n 3dB
Adding Intensities I =I1 + I2, LI = 10 log [(I1 + I2)/I0],
log (y) = x means 10x = y; log (ab) = log(a) + log(b); log (a/b) = log(a) – log(b)
Power P(W), Intensity I(W/m2), and Area(m2); Power = Intensity Area, P = I A
Point Source; Intensity at distance r from a source of power P; I = P/(4r2)
Loudness (phons), Pitch and Timbre; Tempered scale; fn = f0 (1.0595)n
Fourier Spectrum: for complex wave of period T, f1 = 1/T, fn = nf1, and An = amplitude
for triangular wave, odd harmonics only with amplitudes An = A1/n2
for square wave, odd harmonics only with amplitudes An = A1/n
Combining Tones: for f2f1, beating phenomenon, ffused tone = (1/2)(f2 + f1); fbeats = f2 – f1
for f2f1, sidebands, (f2 ± f1)
Hearing: range of hearing 20 Hz to 20 kHz with maximum sensitivity for 1000-4000 Hz
Speech and Singing: acoustic model of vocal tract, fn = n(v/(4L)) for n = 1,3,5,..
String Instruments: Standing waves of harmonic number n (the fundamental is n = 1)
fn = nf1, n = 2L/n, fn = v/n = (n/(2L))√(T/), for n = 1,2,3…
Conversion Factors and Constants
Conversion Factors Constants
1 kg = 1000 gmAcceleration due to gravity
1 m = 100 cm = 39.37 in g = 9.8 m/s2
1 km = 1000 mDensity ( = Mass/Volume)
1 in = 2.54 cm Water = 1000 kg/m3
1 ft = 12 in = 0.305 m Nylon = 1140 kg/m3
1 mile= 5280 ft = 1610 m Steel = 7700 kg/m3
1 s = 1000 msAbbreviations
1 hour = 3600 s mega M = 106
1 N = 1 kgm/s2 kilo k = 103
1 J = 1 Nm = 1 kgm2/s2 milli m = 10-3
micro = 10-6