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
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
A mass of 500 gm is attached to a spring (k = 24.5 N/m) on a
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
(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
ANSWER: -0.19 m (opposite side from
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
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