Module_SP015

o Knowing that : (i) The period, T and frequency, f
depend only on the mass, m and the
  force constant of the spring, k.

  (ii) They do not depend on the
parameters of motion (amplitude).
 
Conditions for the spring-mass system
where executes SHM:
: period of SHM ( unit : s)
: mass attached (unit : kg) 1) The elastic limit of the spring is not
: force constant of the spring exceeded when the spring is being
(unit : N m−1) pulled.

2) The spring is light and obeys Hooke’s
law.

3) No air resistance and surface friction.

Slide 25

MOE50 a block of mass m attached to a spring on a frictionless surface undergoing SHM
MOE51
Ministry of Education, Malaysia; 5/07/2004

when the spring is neiher stretched nor compressed, the block is at the position x = 0 called the equilibrium position of the
system.

MOE52 system oscillates back & forth if disturbed from its equilibrium position.

Ministry of Education, Malaysia; 5/07/2004

when the block is displaced to the right of equilibrium ( x > 0 ), the force exerted by the spring acts to the left.

when the block is at its equilibrium position ( x = 0 ), the force exerted on the spring is zero.

when the block is displaced to the left of equilibrium ( x < 0 ), the force exerted by the spring acts to the right.

Ministry of Education, Malaysia; 5/07/2004

9.3.2 Simple pendulum o The motion occurs in the vertical plane and is
driven by gravitational force.
o A simple pendulum exhibit periodic
motion. It consists of a particle-like bob o The forces acting on the bob are the tension
of mass suspended by a light string and the weight.
of length .
o The tangential component of gravitational
l force is a restoring force which acted on bob
to bring it back to its equilibrium position.

o Assume that angle θ is small (< 10°), use
T approximation
x mP
o Thus:
mg sin  mg cos

mg

o Newton second law:  

 
 

o Is found that : where
 executes linear SHM : period of SHM ( unit : s)
: length of the string (unit : m)
: acceleration due to gravity (unit : m s−2)

o By comparing with : i) Period, T and frequency, f of a simple
pendulum depend only on the length, l of the

  string and the acceleration due to gravity, g.

ii) The period is independent of the mass, m and

the amplitude of oscillation.

o Knowing that : Conditions for the simple pendulum executes SHM are :
1) the angle,  has to be small (less than 10).
  2) the string has to be inelastic and light.

3) only the gravitational force and tension in the string

 

acting on the simple pendulum.

Slide 27

MOE46 The period of a simple pendulum depend only on the length of the string & acceleration due to gravity.

Because the period is indepedent of the mass we conclude that all simple pendulum that are of equal length & are at the same
location ( g is constant ) oscillate with the same period.

Simple Pendulum can be used as a timekeeper & also is a convenient device for making precise measurements of the free fall
acceleration.

Ministry of Education, Malaysia; 6/07/2004

Caution Extra note for better understanding

Some of the reference books use cosine
equation for displacement in SHM such as

The equation of velocity in term of time, t

becomes

And the equation of acceleration in term of

time, t becomes

CHAPTER 10
MECHANICAL AND SOUND WAVES

10.1 Properties of Waves
10.2 Superposition of Waves
10.3 Sound Intensity
10.4 Application of Standing Waves
10.5 Doppler Effect

MODE Face to face Non Face to face 1
SLT SLT
Lecture 2.5
Tutorial 2.5
10
10

LEARNING OUTCOMES

At the end of this topic, students should be able to:

10.1 Properties of waves 10.2 Superposition of waves
(a) Define wavelength and wave number. (a) State the principle of superposition of waves for

(Lecture : C1&C2,CLO1, PLO1, MQF LOD1) the constructive and destructive interferences.

(b) Solve problems related to equation of (Lecture : C1&C2,CLO1, PLO1, MQF LOD1)
progressive wave, , = ( ± )
(b) Use the standing wave equation,
(Tutorial : C3&C4, CLO3,PLO4, CTPS3, MQF LOD6) =

(c) Discuss and use particle vibrational velocity, (Tutorial : C3&C4, CLO3,PLO4, CTPS3, MQF LOD6)
= and wave propagation velocity, = λ
(c) Discuss progressive and standing wave.
(Lecture : C1&C2,CLO1, PLO1, MQF LOD1)
(Tutorial : C3&C4, CLO3,PLO4, CTPS3, MQF LOD6)
(d) Discuss the graphs of:
i) displacement-time, y-t 2
ii) displacement-distance, y-x.

(Tutorial : C3&C4, CLO3,PLO4, CTPS3, MQF LOD6)
(Lecture : C1&C2,CLO1, PLO1, MQF LOD1)

LEARNING OUTCOMES

At the end of this topic, students should be able to:

10.3 Sound intensity (b) Use wave speed in a stretched string, =  
(a) Define and use sound intensity.
(Tutorial : C3&C4, CLO3,PLO4, CTPS3, MQF LOD6)
(Lecture : C1&C2,CLO1, PLO1, MQF LOD1)
10.5 Doppler Effect
(Tutorial : C3&C4, CLO3,PLO4, CTPS3, MQF LOD6) (a) State Doppler Effect for sound waves.

(b) Discuss the dependence of intensity on (Lecture : C1&C2,CLO1, PLO1, MQF LOD1)
amplitude and distance from a point source
by using graphical illustrations. (b) Apply Doppler Effect equation

10.4 Application of standing waves ±f
(a) Solve problems related to the fundamental
and overtone frequencies for: ±
i) stretched string. for relative motion between source and
ii) air columns (open and closed end) observer. (Limit to stationary observer and
moving source and vice versa)
(Lecture : C1&C2,CLO1, PLO1, MQF LOD1)
(Tutorial : C3&C4, CLO3,PLO4, CTPS3, MQF LOD6)
(Tutorial : C3&C4, CLO3,PLO4, CTPS3, MQF LOD6)

Waves

Mechanical wave Electromagnetic waves

Must have a Example : water Do not required a Example: light,
medium waves, sound medium to travel, radio waves,
microwaves,
(matter) to waves, waves on a they can travel infrared, x-ray
travel through string/ rope, waves through a vacuum etc.
in a spring, seismic
at a speed of
waves (Waves 3 m s−1
generated by

earthquakes) etc.

Mechanical wave

Definition
Mechanical waves is defined as disturbance that travels through particles of the medium to

transfer the energy. The particles oscillate around their equilibrium position but do not travel.

A continuous, repetitive disturbance gives rise to a continuous propagation of energy that we call wave
motion.

Based on the Transfer of Energy
o Progressive wave (or travelling waves)
o Standing waves (or stationary waves)

10.1 Properties of Waves

10.1.1 Progressive wave

Definition
Progressive wave is defined as wave that propagated continuously outward from a

source of disturbance.

10.1.2 Terms used to describe waves

Crest

Equilibrium position A

A



Trough

Quantities Definition
Amplitude,
Maximum displacement from the equilibrium position to the crest or
Particle displacement,
Wave displacement, trough of the wave motion.

Vertical displacement of the particle from its equilibrium position.

Distance of particle from the source of disturbance.

Quantities Definition
Amplitude, Maximum displacement from the equilibrium position to the crest or trough of
Frequency, the wave motion.
Period, The number of complete waveforms that pass a given point in one second.

Wavelength, Time for one complete wavefront ( a wavelength) to pass by a given point.
Wave number,
=
Angular
frequency,
i) The distance between two successive crests or troughs.

ii) Distance between any two successive identical points on the wave.

number of waves in a unit distance


=
SI unit:


= =
SI unit : rad s‒1

10.1.3 Equation of progressive waves

where : distance move by a particle from its equilibrium position
: distance of particle from the origin or disturbance
: amplitude of the wave


: wave number ( = )

: angular frequency ( = = )

+ or − : direction of wave propagation

The wave propagates to the left: The wave propagates to the right:

Alternative forms: , = ( ± )


, = λ ( ± )

10.1.4 Particle vibrational velocity and wave propagation velocity

Particle vibrational Wave propagation

velocity, velocity,

Velocity of particle which Wave velocity, is the velocity

oscillate about equilibrium at which wave crests (or other

position in simple harmonic part of waveform) move forward.

motion that generate waves

Wave velocity, is the distance

= = ( sin( ± ) travel by wave profile per unit
String particle time.

Notice that a trough travels a

distance of one wavelength, in

OR a time equal to one period, T.

  Thus the wave velocity is:

Undisturbed
position of
string

= 0 = Varies with time constant

10.1.5 Displacement graphs of the wave

Graph of displacement-time Graph of displacement-distance

() ()

Graph show the displacement of any one Graph shows the displacement of all
particle in the waves at any particular particles in the waves at any particular

distance, from the origin. time

Displacement, Displacement,




from – graph, we can obtain : from – graph, we can obtain :
(1) Amplitude, (1) Amplitude,
(2) Period, (2) wavelength,

Example 1 NON FACE TO FACE SLT

A plane progressive wave is represented by the (b) From equation, = 0.5
equation;

= 20 sin 2 − 0.5 = λ

Where x and y in meter and t is in second. Find λ = = = m
the : .

a) amplitude, (c) From equation, = 2
b) wavelength,
c) period,
=
d) frequency,
= = = s
e) velocity of the wave,
f) direction of wave propagation
g) maximum velocity of the particle.
(d) = = = 1 Hz
= 20 sin 2 − 0.5
Compared with (e) = λ = 1 4 = 4 m s‒1
(f) − : propagate to the right
= sin − (g) = cos ±

(a) amplitude, =20 m = max when cos ± = 1

( ) = = 20 2π
= 40 m s‒1

10.2 Superposition of Waves

10.2.1 Principle of superposition of waves
o Interference is defined as the interaction (superposition) of two or more wave

motions in the same region of space to produce resultant wave.

Principle of superposition of waves

When two (or more) waves are moving in the same region, the resultant
displacement at any point is the vector sum of their individual
displacement at that point.

where and are the displacement of individual pulses at that point

Constructive Interference Destructive Interference

o occurs when the displacements caused by the o occurs when the displacements caused by the
two pulses are in the same direction (ie. both two pulses are in opposite directions.( ie.
are positive/ or negative) One positive, one negative)

o produce a displacement that is larger than the o produce a displacement that is smaller than

displacement of either of the individual waves the displacements of either of the individual
waves.

AA t 0 A
y1 y2 y1
Two approaching A
2A pulses y2
y  y1  y2  A  A  2A
t pults1es y  y1  y2  A  A  0

Two
completely overlap

A A t  t2 A y1A
y2 y1 y2
Emerging pulses
are unchanged

10.2.2 Standing waves (Stationary waves)

Definition
Stationary wave is defined as form of wave in which the profile of the wave does not
move through medium.
a) How to produced stationary waves?
It is formed when two progressive waves of same speed, frequency and

amplitude which are travelling in opposite directions are superimposed.

Animation of a standing wave
(red) created by the
superposition of a left
traveling (blue) and right
traveling (green) wave

b) In observing the stationary wave, there is no sense of motion in the direction of
propagation of either of the original waves (it is called stationary wave because it
does not appear to be travelling).

c) Node (N) is defined as a point at which the displacement is zero, where the
destructive interference occurred.

d) Antinode (A) is defined as a point at which the displacement is maximum
where the constructive interference occurred.



Equation of standing waves

a) Assume two waves with the same amplitude, frequency and wavelength travelling in opposite
directions in a medium:
and

b) Both waves interfere according to the principle of superposition. Therefore,

General wave equation
for a stationary wave

where
cos : amplitude of stationary wave at any position

Note : A given particle in the stationary wave vibrates within the constraints of the envelope
function

: maximum amplitude of stationary wave formed
= 2

: maximum amplitude of the individual progressive waves

(c) Schematic representation of the standing wave (with an indefinite number of nodes and antinodes)
One starts counting the time ( = ) when the displacement y is maximum at =

A AAA AA A

NNNN NN



o The distance between adjacent antinodes is /2.
o The distance between adjacent nodes is /2.
o The distance between a node and an adjacent antinode is /4.
o The amplitude of the vertical oscillation of any particle in the string depends on the horizontal

position, of the particle. Each particle vibrates within the confines of the envelope function
cos

Example 2 NON FACE TO FACE SLT

Two harmonic waves are represented by the
equations below, where , and are is centimetres = 2 → = 2 = 2 = .
and is in seconds. = λ = 0.5 1 = .

= 5 sin( + 2 ) d) Determine the distance between
i. Two adjacent nodes,
= 5 sin( − 2 ) ii. A node and adjacent antinode
a) Write an expression for the new wave when both of the standing wave formed.

waves are superimposed. (i) Distance between adjacent nodes = =

Refer general equation for standing waves
= cos sin ( = 2 )
= ( ) (ii) Distance between a node and adjacent
antinode = =
where , and are is centimetres and is in seconds.

b) Determine the wavelength, frequency and velocity
for both harmonic waves.

2 2
= λ → λ = 2 = .

Distinguish between progressive and standing waves

Progressive wave Standing wave

1 Wave profile move. Wave profile does not move.

2 All particles vibrate with the same amplitude. Particles between two adjacent nodes vibrate with
different amplitudes.

3 Neighbouring particles vibrate with different Particles between two adjacent nodes vibrate in
phases. phase.

4 All particles vibrate Particles at nodes do not vibrate at all.

5 Produced by a disturbance in an elastic medium Produced by the superposition of two waves moving in
opposite direction.

6 Transmits the energy. Energy is not transmitted down the string but “stands”

in place in the string.

(Does not transmit energy)

10.3 Sound intensity

10.3.1 Sound Wave Introduction 4) The distance between the two centre of the
compressions (rarefactions) represent the
1) Sound waves are produced by a vibrating value of wavelength ().
source such as a guitar string, human vocal
cords, prongs of a tuning fork or diaphragm of Compression (high pressure)
a loud speaker. Rarefaction (low pressure)

Direction of wave propagation

λ λ
5) Sound propagates in
2) Sound waves are mechanical and longitudinal
wave which needs a medium for its propagation. three dimension.
Crests of the wave
3) The sound waves propagate in any medium form a series of
through a series of periodic compressions and concentric spherical
rarefactions of pressure, which is produced by the shells (blue circles)
vibrating source. separated by
wavelength. Rays (red
arrows) indicate the
direction of
propagation.

10.3.2 Sound intensity,  perceived by the ears as loudness

Definition

Sound intensity is the energy transported per unit time across a unit area

which is perpendicular to the direction of wave propagation.

Equation OR Intensity of a sound wave is uniformly
distributed at the same distance. For
OR 3D waves, the area a sound wave
travel through is a sphere

where
: Intensity of sound wave
: Power of sound wave

: Energy of the sound Sound Sound
power, intensity,
: area of a sphere of radius, through which
the sound energy passes perpendicularly

: time

o Intensity is a scalar quantity. Its SI unit is watt per meter square (SI Unit: )

Dependence of sound intensity, I on:

① Amplitude,

o Intensity is directly proportional to the square of the wave amplitude:

o Small amplitude corresponds to low energy wave, low intensity

o Large amplitude corresponds to high energy wave, high intensity

Amplitude Graph of Intensity against Graph of Intensity against
amplitude the square of amplitude
Quieter ( against A)
( against )

I ( ) I ( )
=


0 0 ( )

Louder

Distance from point source,

o The intensity of a sound decreases as you get farther from the source of sound. Intensity is
inversely proportional to the square of the distance from point source

From : Graph of intensity against Graph of against
the square of distance

( against )

I ( ) I ( )
= 4
= 4

0 ( ) 0 1
o As distance, increases, ( )

The relationship can be illustrated by the figure above. intensity, decreases.
The energy twice as far from the source is spread =
over four times the area, hence one-fourth the
intensity.

Example 3 NON FACE TO FACE SLT

A small source emits sound waves with power c) At what distance would the intensity be one-
output 80.0 W. fourth as much as it is at = 3.00 ?

a) Find the intensity 3.00 from the source.

Given : =80.0 W ; Find : =?
80
Write in mathematic:
= 4 = 4 (3) =
= . W m−2

¼ = (3)

b) Find the distance at which the intensity of the = m
sound is 1.00 × 10

Concept : power of the sound source, is
constant


= 4

1.00 × 10 = → = .

10.4 Application of standing waves

Formation of Standing waves

In general, standing waves are set up Stretched They are set up in the air
in the strings of musical instruments string
Air column column in an organ pipe, a
(ex: guitar, violin) trumpet or a clarinet when
when plucked, bowed or struck. air is blown over the top.

Open end
(both ends open)

Closed end
(One end is closed)

10.4.1 Formation of standing waves in stretched string

o When a string of length stretched between o The wave and its reflection wave interfere
2 fixed ends is plucked and then released. according to the superposition principle and
produce standing wave.
o Transverse waves produced travel down
towards the fixed ends & reflected back. o Speed of wave on a stretched string is:

o Wave pulse is being inverted when reflected.  

where )
: Speed of wave on a string
: Tension in the string
: Mass per unit length of the string ( =

o For a stretched string, we can set up a
standing wave patterns at many frequency.
The more loops, the higher the frequency.

Mode Standing wave pattern Frequency The standing wave on the string forced the
Fundamental surrounding air vibrates and produces a
(1st harmonic) The simplest standing sound wave in the air.
wave has one node at each = If the string vibrating in the fundamental
= end, and no more. mode hence the sound wave produced is
in the fundamental tone.
=
1st Overtone Next possible standing wave we can make Equation
(2nd harmonic) has an additional node in the center.
= In general
= OR

=
=
where   ;

=

2nd Overtone The third possible standing wave has two : speed of wave in a stretched string
(3rd harmonic) nodes in addition to the nodes at the end. = : mass per unit length
=
= (unit for : kg m−1)

: length of the stretched string
: 1, 2, 3, 4, ...

F 1st O 2nd O 3rd O

10.4.2 Formation of standing waves in air columns (open and closed end)

1) Standing waves can be set up in a tube of air (air column),

such as an organ pipe, as the result of interference
between sound waves travelling in opposite
directions.

2) The relationship between the incident wave and the
reflected wave depends on whether the reflecting end of
the tube is open or closed.

i) If one end is closed, a node (N) must exist
at that end because the movement of air
is restricted.

ii) If the end is open, the elements of air have
complete freedom of motion, and an
antinode (A) exists.



3) Air column open at both ends Mode Standing wave pattern Frequency

Table shows the first three standing Fundamental
wave pattern for a pipe of length , open (1st harmonic) =
at both ends.
=
=
The simplest standing
wave has antinode at
both ends, and one =
node at the center.

Equation 1st Overtone Next possible standing wave we can make =
(2nd harmonic) has an additional antinode in the center. =
In general
=
OR =


: speed of sound in air 2nd Overtone =
: length of the air column (3rd harmonic) =
: 1, 2, 3, 4, ...
=
F 1st O 2nd O 3rd O The third possible standing wave has two
antinodes in addition to the antinodes at the
end.

Air column open at both ends, all
harmonics are present.

4) Air column closed at one end Mode Standing wave pattern Frequency

Table shows the first three standing wave Fundamental
pattern for a pipe of length , closed at =
one end. (1st harmonic)

= =

The simplest standing
wave has a node at =
the closed end and
antinode at open end
=
Equation =

In general 1st Overtone Next possible standing wave we can make
(3rd harmonic) has an additional pair of node and antinodes. =

OR =
=
: speed of sound in air =
: length of the air column
: 1, 3, 5, 7, 9, ...

F 1st O 2nd O 3rd O 2nd Overtone The third possible standing wave has two pair
(5th harmonic) of nodes and antinodes in addition to the node
and antinode at the ends
=

Air column closed at one end; only odd

harmonics are present

Hints in drawing standing wave pattern formed:

Remember the fundamental pattern for the three cases :

Stretched string Open ends air column Closed end air column

For overtones , use method. Multiply the fundamental pattern

according to the corresponding harmonic number

Let’s try it out : Sketch standing wave pattern for third overtone in a closed end pipe.

① Identify the corresponding ② Divide the pipe into 7 portion

harmonic number for fifth overtone ① ②③ ④ ⑤⑥ ⑦

F 2nd O

Closed end : = 1, 3, 5, 7, 9 …

1st O 3rd O N AN A N A N A

third overtone  = 7 ③ use × and multiply the fundamental pattern 7th times.
④ Label all the N and A positions.

Example 4 NON FACE TO FACE SLT
Solution
A stretched wire of length 80.0 cm and mass Given : = 80 cm = 0.8 m ; = 12 = 0.012 kg
12.0 g vibrates transversely. Waves travel (a)
along the wire at speed 220 m s-1. Three
antinodes can be found in the stationary (b)(i) refer to the standing wave pattern formed in (a)
waves formed in between the two fixed ends 2 2(0.8)
of the wire. 3 → λ = 3 = 3 = .
= 2 λ
a) Sketch and label the waveform of the
stationary wave. (ii)

b) Determine ()
(.)
i) The wavelength of the progressive
wave which move along the wire. (iii) =   ; =

ii) The frequency of the vibration of the
wire.
=   → = = ( . ) = N
iii) The tension in the wire.
.

Example 5 NON FACE TO FACE SLT

A section of drainage culvert 1.23 m in length (b) What are the three lowest natural frequencies
makes a howling noise when the wind blows. of the culvert if it is blocked at one end?
(a) Determine the frequencies of the first three
Solution
harmonics of the culvert if it is open at both
ends. Take = 343 m s−1 as the speed of Given : = 1.23 m ; = 343 m s−1
sound in air.
The fundamental frequency of a pipe closed at
Solution one end is

Given : = 1.23 m ; = 343 m s−1 ( )( ) Hz
(. )
frequency of the first harmonic of a pipe
open at both ends is

( )( ) Hz In this case, only odd harmonics are present;
(. ) hence, the next two harmonics have frequencies

Because both ends are open, all harmonics are =

present; thus, = = 3 = 2 69.7 =209.1 Hz

= 2 = 2 139 = Hz = 5 = 3 69.7 = . Hz

= 3 = 3 139 = Hz

(c) For the culvert open at both ends, how many Physics of the stringed musical NON FACE TO FACE SLT
of the harmonics present fall within the normal instruments is very simple. The notes
human hearing range (20 to 17 000 Hz)? played depend upon the string which is
disturbed. The string can vary in length,
Solution its tension and its linear density (mass /
length).
Because all harmonics are present, we can
express the frequency of the highest harmonic
heard as = where is the number of
harmonics that we can hear.
For = 17000 Hz, we find that the number of
harmonics present in the audible range is

=

17000
= = 139

=

In real world, only the first few harmonics are of A flute is an Open-Open tube.
sufficient amplitude to be heard.

Resonance in air column

Air column

Audio frequency generator

Loudspeaker

1) The loudspeaker emits sound of a certain frequency which can be changed.
2) Vibration of the diaphragm of the loudspeaker forces the air in the tube into

vibration.
3) When the frequency of the vibration of the loudspeaker equals to

fundamental frequency of the air column, resonance occurs.
4) A sound of high intensity (perceived by ears as loud sound) is produced at

this frequency.

10.5 Doppler Effect

Have you ever experience these?

i) You may have noticed that you hear the pitch of the siren on a speeding fire truck drop abruptly as it passes
you. OR

ii) You may have noticed the change in pitch of a blaring horn on a fast moving car as it passes by you. OR
iii) The pitch of the engine noise of a race car changes as the car passes an observer.

When a source of sound is moving toward an Higher pitch Lower pitch
observer, the pitch the observer hears is higher
than when the source is at rest; when the source is
travelling away from the observer, the pitch is
lower. This phenomenon is known as the Doppler
Effect and occurs for all type of waves.

Definition

Doppler Effect is defined as the change in the apparent (observed) frequency of a
wave as a result of relative motion between the source and the observer.

Explanation of Doppler effect phenomenon

1) When there is no relative motion between source and observer, all observers hear same
frequency.

Speed of sound,
is constant
λλ
= λ


→ = λ
Same λ ;
same

2) Movement of the source alters the wavelength and the received frequency of
sound, even though source frequency and sound velocity are unchanged.

Hears sound of Hears sound of shorter
longer wavelength, wavelength, higher
lower frequency, frequency, higher pitch.
lower pitch.

3) As the source moves 4) As the source
away from observer, approaching
the same number of observer, the same
waves are number of waves are
expanded to fill a compressed into a
larger distance.
From : = , small distance.
From : = ,
As constant, ∝
As constant, ∝
thus λ ↑  f ↓
thus λ ↓  f ↑

λλ

General equation used to calculate How to use OS method to determine
apparent frequency : the correct + or ‒ sign in the general
equation?

Example : Moving observer approaches
stationary source

–OS+
where –OS+
: Speed of sound.
: Speed of source.

: Speed of observer.

: Apparent frequency or observed
frequency.

: Frequency of the source or actual
frequency

How to use OS method to determine the correct + or ‒ sign in the general
equation?

Example : Moving observer Example : Moving source Example : Moving source
receding stationary approaches stationary receding stationary
source observer observer

–OS+ –OS+ –OS+




Graph of apparent frequency against Example 6 NON FACE TO FACE SLT
distance travelled
The siren of a police car at rest emits at a
(Hz) predominant frequency of 1600 . What frequency
will you hear if you are at rest and the police car
approaches moves at 25 toward you. Given that the
speed of sound in air is 345 .

Move away Solution

Given : = 1600 Hz ; = 25 m s−1

(m) = ± –OS+
±
Stationary observer

As source moves closer (approaches) the observer,
= −
>
At the moment source crosses observer, apparent
frequency, = = −
As source moves away from observer, <
= Hz

z TOPIC 11 MODE Face to Non
Deformation of solids face Face to
Lecture SLT
11.1 Stress and strain Tutorial face
11.2 Young’s modulus 2.5 SLT

2 2.5

2