1] An unknown mass
is attached to a spring on a horizontal, frictionless surface.
The mass
is released from rest at a position 20.0 cm from the equilibrium
position
and then
oscillates with a frequency of 1.25 Hz.
What is
the speed of the mass at a position 10 cm from the equilibrium position?
ANSWER: 1.36 m/s
2] The third
harmonic frequency produced by both a stretched string and an organ
pipe closed at one end is 1320 Hz. Assume the air temperature
is 20oC and that
the speed
of the wave on the string is 1/2 the speed of sound in
air.
A) Sketch the standing wave pattern for
this third harmonic frequency in both the
string and the organ pipe with one end closed.
ANSWER: see text for figures of these patterns
B) Determine the length each device
must have to produce the frequency described
above.
ANSWER: both will have a length of 0.195 m
C) What is the wavelength of the fundamental frequency for each device?
ANSWER: string, 0.39
m pipe, 0.78 m
3]
A mass of 500 gm is attached to a spring (k = 24.5 N/m) on a
horizontal, frictionless
surface. A force of 4.90 N pulls the mass to the right, displacing it
some distance, x,
from its equilibrium position. The mass is then released and oscillates
in simple
harmonic motion.
(A) What is the maximum speed of the mass for this motion?
ANSWER: 1.4 m/s
(B) What is the position, x, of the mass 0.500
seconds (this is time, t) after it is
released?
ANSWER: -0.19 m (opposite side from
release point)
4] Speakers
designed for a large auditorium can emit sound waves with a power of 300
watts. The area of the speaker cone from which the waves are
emitted is 0.500 m2.
What is
the intensity level , in decibels, right next to this speaker?
ANSWER: 148 dB
6] A piano string
with a mass per unit length of 0.0025 kg/m is put under a tension of
350 N in
order to produce a standing wave with a frequency of 645 Hz. What must
be the
length of the string?
ANSWER: 0.290 m
7] The amplitude
of the simple harmonic motion for a mass suspended on a spring
is
25.0 cm. The mass has a speed of 1.12 m/s when it is at a point
10 cm from its
equilibrium position. Determine the total energy for this system
if the mass is 300
grams.
ANSWER: 0.224 J
8] When placed
against the ear, a speaker from a set of headphones is essentially
emitting
sound directly in contact with the ear drum ( surface area = 0.50 cm2
). If
the sound
level is not to exceed 100 dB at the ear drum, what is the maximum power
that the
speaker can radiate? (I0 = 1.0 x 10-12 W/m2 )
ANSWER: 5.0 x 10-7 W