**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 20^{o}C 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 m^{2}.

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 cm^{2}
). If

the sound
level is not to exceed 100 dB at the ear drum, what is the maximum power

that the
speaker can radiate? (I_{0} = 1.0 x 10^{-12} W/m^{2 })

ANSWER: 5.0 x 10^{-7} W

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

ANSWERS:

1. B

2. C

3. C

4. E

5. A