Name: _______________,____________
(PRINT)
(last)
Seat #:
____________________
(first)
ID#: _______________
Name:
____________________
(SIGNATURE)
P105 Basic Physics of Sound
IU Physics Dept., Spring 2005
Test #2
March 25, 2005
Instructions:
1. Please do not start the exam until instructed!
2. Print your Name and ID# and sign your NAME at the top of this page.
3. Calculators are allowed. No books or notes are allowed. Please leave your
course materials at the rear of the room.
4. 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.
5. 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.
8. 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
1
8
2
8
3
8
4
8
5
8
6
12
7
12
8
12
9
12
10
12
Total
100
Score
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
(a)
__________________
(b)
Intensity
(c)
__________________
Sensation
and
Pitch
and
__________________
and
Timbre
Q3. What are formants, and why are they important?
Q4.
(a) Three pure tones with frequencies of 200 Hz, 800 Hz and 1000 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, 800 Hz and 1050 Hz are played together.
Is a virtual pitch heard? If so, at what frequency? If not, why not?
Q5.
(a) What is the name of the spiral-shaped organ in the inner ear that contains the
basilar membrane?
________________
(b) What is the role of the basilar membrane in hearing ?
II. Problems: 60 points (Show your work to receive fill 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 9.5  10-3 N/m2 at a distance of 5 meters from the source.
(a)
What is the pressure level Lp of the sound wave (in decibels)?
(b) What is the sound intensity (in W/m2) at this location?
(c) What is the sound intensity level LI (in decibels)?
(d) 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
3 meters from the source to have an intensity level of 43 dB.
(a) Supposed the sound power produced by the source is increased by a factor of 20.
What is the new intensity level (in dB) of the sound at 3 meters from the source?
(b) What is the new intensity of the sound in W/m 2 at this location?
(c) What is the intensity of this sound in W/m2 at a distance of 9 meters?
P3. A complex tone consisting of a square wave with a period of 0.005 s 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 (amplitude versus time) corresponding to these two pure tones.
(c) What is the ratio of amplitudes AB/AA for these two tones?
P4. Singing at the top of his voice a tenor can produce a sound level of 120 dB.
(a) What is the sound intensity that corresponds to this sound level?
(b) For an open mouth area of 25 cm2, what is the total radiated sound power?
(c) Use the acoustic model of the vocal tract as a pipe closed at one end to determine
the length of the region in the larynx that allows the tenor to produce his “singer’s
formant” in the region of 2500 Hz.
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 three semitones?
Equation Sheet for Test #2
Equations
Energy: kinetic energy KE = (1/2)mv2; potential energy PEgrav = mgh & PEspr = (1/2)Ky2
Work and Energy: Work = Force  distance; W = Fd; Work done = KE
Conservation of energy: KE + PE = constant = Etotal = (1/2)m(vbot)2 = mghtop
Periodic motion: frequency f (Hz); period T (s); f = 1/T; amplitude A; PEmax = (1/2)KA2
Mass on spring: Fsp = - Ky, 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 tC) m/s -> at 20C 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, f2  f1, 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 LI = 10 log [(I1 + I2)/I0],
log (y) = x means 10x = y; log (ab) = 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/(4r2)
Loudness (phons), Pitch and Timbre; Tempered scale; f n = 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 A n = A1/n2
for square wave, odd harmonics only with amplitudes A n = A1/n
Combining Tones: for f2  f1, beating phenomenon, ffused tone = (1/2)(f2 + f1); fbeats = f2 – f1
for f2 >> f1, 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
1 kg
= 1000 gm
1 m = 100 cm = 39.37 in
1 km
= 1000 m
1 in
= 2.54 cm
1 ft =
12 in = 0.305 m
1 mile = 5280 ft = 1610 m
1 s = 1000 ms
1 hour = 3600 s
1 N = 1 kgm/s2
1 J = 1 Nm = 1 kgm2/s2
Constants
Acceleration due to gravity
g = 9.8 m/s2
Density ( = Mass/Volume)
Water = 1000 kg/m3
Nylon = 1140 kg/m3
Steel = 7700 kg/m3
Abbreviations
mega M = 106
kilo
k = 103
milli
m = 10-3
micro  = 10-6
Figures