Problems
179
shear modulus of soft fatty tissue. (Assume the shear modulus is much larger than
the bulk modulus, due to the difficulty in compressing water in tissue.)
5.5 Knowing that air has an effective molecular weight 7.24 times that of helium,
and that the ratio of specific heats for helium is 1.67 while that of air is the 1.4, how
many octaves above your regular speech will your voice sound when you breathe
helium instead of air before speaking?
5.6 Is it always possible to decompose a given voice pattern (giving wave amplitude
over a segment of time) into Fourier components? If so, what might the various
Fourier components tell us? If we are given the Fourier components, can we always
reconstruct the voice pattern?
5.7 Suppose a wave is found to have a dispersion relation ω = c
k 2 + k 2
o , where
k o and c are constants. Show that the phase velocity for this wave is related to the
group velocity by v g = c 2 /v p .
5.8 Find the intensity of sound in air if the sound level is 65 dB.
5.9 If you hear a pure note of frequency 512 Hz with a level of 65 dB at your ear,
what is the amplitude of the air vibration?
5.10 A 60 dB sound is sustained in a room with a size of 5 m by 6 m by 3 m. How
much sound energy is contained in that room at any one time?
5.11 Suppose an ultrasonic wave is produced in the air and arrives at your skin
perpendicular to the surface. Estimate the percent of the energy of that wave
reflected back into the air.
5.12 If an ultrasonic wave goes from the air to tissue (with a speed four times that
of air), what is the maximum angle of incidence?
5.13 If ultrasonic wave of frequency 2 MHz travels through muscle tissue, how far
will the wave travel before being reduced to half its initial intensity.
5.14 If the skin of an abdomen has a sound impedance of 1.4 × 10 5 g/(s cm 2 ) while
that of the surrounding air is 4 g/s cm 2 , what percent of sound intensity arriving at
the skin from the air enters the abdomen?
5.15 If a 4 × 3 m 2 wall of a room has a sound impedance of 3 × 10 5 g/(s cm 2 )
(the figure for air is 4 g/(s cm 2 )), how much sound power enters the walls, with an
incident sound at 50 dB?
5.16 If some energy of an ultrasonic wave goes from the air to tissue (with a speed
four times that of air), what is the maximum angle of incidence?
5.17 A acoustical converging lens typically has two concave sides, in contrast to
an optical converging lens. Why are they so different in shape compared to optical
lenses?
179
shear modulus of soft fatty tissue. (Assume the shear modulus is much larger than
the bulk modulus, due to the difficulty in compressing water in tissue.)
5.5 Knowing that air has an effective molecular weight 7.24 times that of helium,
and that the ratio of specific heats for helium is 1.67 while that of air is the 1.4, how
many octaves above your regular speech will your voice sound when you breathe
helium instead of air before speaking?
5.6 Is it always possible to decompose a given voice pattern (giving wave amplitude
over a segment of time) into Fourier components? If so, what might the various
Fourier components tell us? If we are given the Fourier components, can we always
reconstruct the voice pattern?
5.7 Suppose a wave is found to have a dispersion relation ω = c
k 2 + k 2
o , where
k o and c are constants. Show that the phase velocity for this wave is related to the
group velocity by v g = c 2 /v p .
5.8 Find the intensity of sound in air if the sound level is 65 dB.
5.9 If you hear a pure note of frequency 512 Hz with a level of 65 dB at your ear,
what is the amplitude of the air vibration?
5.10 A 60 dB sound is sustained in a room with a size of 5 m by 6 m by 3 m. How
much sound energy is contained in that room at any one time?
5.11 Suppose an ultrasonic wave is produced in the air and arrives at your skin
perpendicular to the surface. Estimate the percent of the energy of that wave
reflected back into the air.
5.12 If an ultrasonic wave goes from the air to tissue (with a speed four times that
of air), what is the maximum angle of incidence?
5.13 If ultrasonic wave of frequency 2 MHz travels through muscle tissue, how far
will the wave travel before being reduced to half its initial intensity.
5.14 If the skin of an abdomen has a sound impedance of 1.4 × 10 5 g/(s cm 2 ) while
that of the surrounding air is 4 g/s cm 2 , what percent of sound intensity arriving at
the skin from the air enters the abdomen?
5.15 If a 4 × 3 m 2 wall of a room has a sound impedance of 3 × 10 5 g/(s cm 2 )
(the figure for air is 4 g/(s cm 2 )), how much sound power enters the walls, with an
incident sound at 50 dB?
5.16 If some energy of an ultrasonic wave goes from the air to tissue (with a speed
four times that of air), what is the maximum angle of incidence?
5.17 A acoustical converging lens typically has two concave sides, in contrast to
an optical converging lens. Why are they so different in shape compared to optical
lenses?