Download Topic 4 New Part 1 Oscillations and Waves solutions

Solutions Topic 4 Part 1 Oscillations and Waves
Webquest
WEBQUEST – Use the links below to answer the questions.

What is a Wave? - a disturbance which travels through
a medium. Q 1
Physics students loving the study of
waves

Longitudinal and Transverse Waves - Particle Motion for
Longitudinal, Transverse, and Water Waves. Q 2-3 & 5

Categories of Waves Only need to read first section that covers compressions & rarefaction.
Stop once you get down to wavelength. Q 4

Introduction to Waves Deal with the amplitude & wavelength of waves. Q 6

Parts of a Wave - Shows the parts of a transverse wave. Q 6-8
QUESTIONS:
1. What is a mechanical wave? How are waves created? Compare the direction of energy transfer
and particles movement?
Mechanical Waves are waves which propagate through a material medium (solid, liquid, or gas)
at a wave speed which depends on the elastic and inertial properties of that medium. Light
waves are not mechanical waves
wave is a disturbance or variation which travels through a medium
2. Define longitudinal & transverse waves by describing how the particles are move relative to the
direction of energy propagation (i.e. the direction the wave is traveling).
Longitudinal – back and forth or parallel to direction of motion
transverse – up and down or perpendicular to direction of motion
water – clockwise circles
3. Identify examples of longitudinal and transverse waves.
sound, light
4. What are the areas of compression and rarefaction found on longitudinal waves? Define peak
and trough for transverse waves.
compression – vibrating particles are being compressed = high energy = high density
rarefaction – vibrating particles are decompressed or spread out = low energy = low density
5. Define amplitude and wavelength for both wave types.
amplitude = height of the wave or maximum positive displacement
wavelength = crest to crest or trough to trough compression to compression or rarefaction to
rarefaction
6. Define the frequency of a wave and explain how wave frequency is measured.
number of waves per sec = Hz = s-1
7. What is the period of a wave? Identify how the period of a wave relates to its frequency.
T = duration of wave, how long the wave lasts T = 1/f
8. What factors affect the speed at which a wave travels? State the relationship between wave
speed, frequency and wavelength.
medium: more dense slower the wave v = λ f
1. Kinematics of Simple Harmonic Motion (SHM)
Packet Examples
Example 1 : In fig. 1.1 above , it takes the pendulum 5 seconds to complete one cycle. What is
the period (T) ? What is the frequency (f) ?
T = 5s
f = 1/ T = 0.20 Hz
Example 2: a metal rod is struck and it starts to vibrate back and forth. If it vibrates 30 times per
second what is the frequency? The period?
f = 30Hz
T = 1/30 = 0.03 s
Example 3 : A) If a particle undergoes SHM with amplitude equal to 0.18m, what is the total
distance it travels in one period? B) If it takes 3 seconds to complete one cycle what is the
period? what is the frequency?
A) T = 4A
4 x .18 = .72 m
B) T = 3s
f = 1/3 = 0.33Hz
May 2009 #13 Paper 1
For a system executing simple harmonic motion, the restoring force acting on the system is
proportional to the
A. displacement of the system from equilibrium
B. amplitude of oscillation
C. elastic potential energy
D. frequency of oscillation
A F = -kX
May 2009 # 12
Ans. B
SIMPLE HARMONIC MOTION takes place when an object ( particle) that is disturbed away
from its fixed equilibrium position experiences an acceleration and force that is proportional
and OPPOSITE to its displacement.
In general to check whether SHM will take place we must check that :
1. There is a fixed equilibrium position
2. Acceleration and force must be opposite and directly proportional to
displacement : a ~ -x
Example packet
A pendulum completes 10 swings in 8s. Calculate the period, frequency and angular frequency.
T = time for one swing = 8s / 10 swings = 0.8 s
f = 1/T = 1/ 0.8 = 1.25 Hz

2
T
ω = 7.85Hz = s-1
2. Graphical Analysis of SHM
EXAMPLE Packet
The graph below shows the variation with time t of the displacement x of a particle undergoing
simple harmonic motion.
Which graph correctly shows the variation with time t of the acceleration a of the particle? B
B - . amax follows xmax BUT OPPOSITE IN DIRECTION and occurs at T/2 and T. This is where
the restoring force is at its max and corresponds to max acceleration.
3. Relating SHM to Linear Graphs
a vs. X
a = - ω2 x
May 2009 Alternative # 13
A - amax follows xmax BUT OPPOSITE IN DIRECTION
Observe that the slope is negative , –ω2 , and a is opposite in direction to X. In other words,
when a is positive X is negative and vice versa.
Tsokos p. 211 : 15
p. 203 Q5 a, b only
A) The graph is a straight line through the origin with a negative slope and fits the
defining relation for SHM a = –ω2 x, where –ω2 is the slope.
B) As can be seen from the graph below the maximum displacement X is - 6.0 cm = - 0.06 m
and this = Amplitude .
–ω2 is the slope and from calculating it from the graph gives :
–ω2 = ∆y = 1.5 – 0
∆x
= - 25 
ω =√25 = 5.0 s-1
- 0.06 – 0
Note X is in cm and must convert to meters
Note unit is s-1 = m s-2
m
ω = 5.0 s-1
T = 2π = 1.3s
ω
=
s-2
 √s-2 = s-1
p. 211 16 a and b only
p. 211 16 c
4. Energy in Simple Harmonic Motion pp. 204-207
Example The graph shows how the velocity v of an object undergoing simple harmonic motion
varies with time t for one complete period of oscillation.
Which of the following sketch graphs best shows how the total energy E of the object varies
with t?
During an oscillation the energy transforms between potential and kinetic. But Total Energy
stays the same see # 8 review qs.
Example : A transverse wave travels from left to right. The diagram below shows how, at a
particular instant of time, the displacement of particles in the medium varies with position. Which
arrow represents the direction of the velocity of the particle marked P?
P. 206 Q9
Try these p. 30 of packet
Try these :
1. A 10 kg mass is attached to a spring and undergoing SHM. If the maximum
kinetic energy it obtains is 70 J calculate the maximum speed the mass obtains?
change
2. A 5 kg mass is attached to a spring and undergoing SHM.The amplitude is
0.05m . If the maximum potential energy the mass obtains through an oscillation
is 100 J, calculate the period of oscillation.
Example packet
A wooden block is at rest on a horizontal frictionless surface. A horizontal spring is attached
between the block and a rigid support.
The block is displaced to the right by an amount X and is then released. The period of
oscillations is T and the total energy of the system is E.
For an initial displacement of
X
which of the following shows the best estimate for the
2
period of oscillations and the total energy of the system?
Period
A.
T
B.
T
C.
D.
T
2
T
2
Total energy
E
2
E
4
E
2
E
4
B
The period ( T ) is independent of amplitude (A) or displacement (X). The energy is
proportional to A2 or X2 since Ep = ½ k x2.
T for X or X is the same.
2
Total energy of system E for X = 1 E
If X is decreased by ½ (X ) the total energy is decreased by (1/2)2 = 1/4
2
So total energy of system is = E
4
IB Exam May 2009 # 14 Paper 1 p. 33 of packet
A
The period ( T ) is independent of amplitude (A) or displacement (X). The energy is
proportional to A2 or X2 since Ep = ½ k x2.
T for X or X is the same.
2
Total energy of system E for X = 1 E
If X ( or A) is doubled (2A) the total energy is increased by (2)2 = 4
So total energy of system is = 4 E
5. Damping pp. 207 – 209
IB Exam May 2009 # 15 Paper 1p. 37 of packet
C
6. Travelling Wave Characteristics pp. 216 - 225
Example 1 packet
A transverse travelling wave has amplitude A0 and wavelength λ.
The distance between a crest and its neighbouring trough, measured in the direction of
energy transfer of the wave is equal to
A.
A0.
B.
2A0.
C.

.
2
D.
λ.
Ans. C
Example 2 packet
One end of a long string is vibrated at a constant frequency f. A travelling wave of wavelength 
and speed v is set up on the string.
The frequency of vibration is doubled but the tension in the string is unchanged. Which of
the following shows the wavelength and speed of the new travelling wave? A
Wavelength
A.
B.
λ
2
λ
2
Speed
v
2v
C.
2
v
D.
2
2v
v=λf
wavelength is inversely proportional to f. speed stays the same
Example 3 packet
A wave is travelling through a medium. The diagram shows the variation with time t of the
displacement d of a particle of the medium from t = 0 to t = 25 ms.
1.5
1
d/cm
0.5
00
5
10
15
20
25
t/ms
–0.5
–1
–1.5
Which of the following correctly gives the frequency and the amplitude of the wave? D
frequency / Hz
amplitude / cm
A.
2.0  10–2
2.0
B.
2.0  10–2
1.0
C.
50
2.0
D.
50
1.0
f = number of waves per second
or f = 1/T
period (T) = duration of 1 wave
by looking at graph one wave is from crest to crest and it takes 20 ms = T = 0.02 s
f = 1/T = 1/0.02 = 50s-1 = 50 Hz
Tsokos p. 225 - 226: 3, 7, 8 add ( speed of sound = 330 ms-1)
7. The Electromagnetic Spectrum
a. COMPLETE : Table 4.4.1 The Electromagnetic Spectrum
Radiation Type
Order of
magnitude of
wavelength (m)
Order of
magnitude of
frequency (Hz)
Practical applications or
uses
Radio waves
10-3
104
radio
Microwave
10-2
108
microwave
Infrared
10-5
1012
sight
Visible light
10-6
1015
Colors, sight
Ultra violet UV
10-8
1016
Insect sight,
X-rays
10-10
1018
medicine
Gamma ray
10-12
1020
Atomic , nuclear energy
Detection
method
b. List the colors of the visible spectrum in order of increasing wavelength.
ROY G BIV