SAMPLE OLD EXAM PROBLEMS for Chapters 13 & 14

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?

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?

(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?

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?

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.

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 )

MULTIPLE CHOICE

1.  Standing waves can be formed if the co-incident waves in the medium
A.  have the same direction of propagation
B.  have the same frequency
C.  have different amplitudes
D.  have different wavelengths

2.  The frequency heard by a sound detector is higher than the frequency emitted by the source.
Which of the statements below must be true?
A.  the source must be moving away from the detector
B.  the source must be moving towards the detector
C.  the source or the detector or both are moving towards each other
D.  the detector must be moving away from the source

3.  Two wave pulses are moving towards each other along a string.  When they meet, a larger amplitude
pulse is observed.  The phenomenon that happened is called
A.  reflection
B.  refraction
C.  constructive interference
D.  destructive interference

4.  Which quantities are considered constants for simple harmonic motion?
A.  position and speed
B.  acceleration and speed
C.  position and angular frequency
D.  amplitude and speed
E.  amplitude and frequency

5.  A mass on a spring is undergoing simple harmonic motion.  At the instant when the mass passes through
the equilibrium position for the spring, it posseses
A.  only kinetic energy
B.   only potential energy
C.  both kinetic and potential energy in equal amounts
D.  more kinetic energy, but some potential energy
E.  more potential energy, but some kinetic energy