Sound Waves

Montfort College Secondary Section English Program M5 Physics

Name _________________________ M5A Number ________
 Sound waves
✔ Sound waves are longitudinal waves which may propagate in solids,
liquids and gases. They can not travel in vacuum.
✔ The speed of sound depends on the nature of the medium in which it
travels.
✔ Sound propagates much faster in liquids and solids than it does in gases.
✔ Sound waves produce variation of the density and pressure of the medium
along the direction of propagation. Traveling low density and high density
sections are called rarefactions and compressions, respectively.
https://www.youtube.com/watch?v=GkNJvZINSEY
For human being the audible range of sound wave is from 20 Hz to 20
KHz.

The speed of sound waves

The speed of sound in air is affected by temperature. At standard pressure
and temperature ( at 00C and 1atm pressure) the speed of sound is 331
m/s.
The speed of sound in air is :
V = ( 331 + 0.606 Tc) m/s
Tc is air temperature in degree Celsius.
The speed of sound in air increases 0.606 m/s for each degree Celsius
increase in temperature.
Exercise 1. Find the speed of sound in air at 200C?
2. The velocity of sound in air at 00C is 331 m/s. At what temperature will the
velocity becomes 360m/s?

Speed of Sound
Medium Velocity (m/s)

air (200 C) 343

air (00 C) 331

Water (25 C) 1493

Sea water 1533

Diamond 12000

Iron 5130

Copper 3560

Glass 5640
 Reflection of sound
The reflection of sound on a boundary is called echo.
𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑡𝑟𝑎𝑣𝑒𝑙𝑙𝑒𝑑
The speed of sound =
𝑡𝑖𝑚𝑒 𝑡𝑎𝑘𝑒𝑛
𝟐𝑺
V=
𝒕
The reflection of sound helps to determine the depth of a sea.
Exercise1. A ship sends out a sound wave and receives an echo after 1
second. If the speed of sound in water is 1500 m/s, how deep is the
water?
2. A person clapped his hands near a cliff and heard the echo after 4 s. What is
the distance of the cliff from the person if the speed of the sound, v is taken
as 346 m/s? What is the temperature of the air?

3. A person at a fireworks display times the lag between seeing an explosion

and hearing its sound, and finds it to be 0.5 s. How far away is the
explosion if air temperature is 20ºC and if you neglect the time taken for
light to reach the person?
 Intensity of sound waves
Intensity is the average energy transferred per second divided by the area.

𝑃𝑎𝑣
I=
𝐴

A = 4πr2
Ex: A point source radiates energy uniformly in a spherical pattern at a
rate of 12.56W. What is the intensity of sound energy at a distance of
100m from the source?
2. The intensity of sound from a point source at a distance of 100m is 10-6
W/m2. What is the intensity from the same source at a distance of 50m?

Home work
1. A sound source emits a sound towards a reflecting object, and the wave
returns to the source in 1.4 sec. If the temperature of the air is 360C,
A) What is the speed of sound at 360C?
B) How far away is the object from the source?
2. What is the sound power (the energy per second) incident on the eardrum
at 6 x 10-6 W/m2 intensity of sound? The area of eardrum is equal to 5 x 10-5
m2.

Sound Intensity level

 The most common approach to sound intensity measurement is to use the
decibel scale.
 Decibels measure the ratio of a given intensity I to the threshold of hearing
intensity , so that this threshold takes the value 0 decibels (0 dB).
Intensity Level in decibels
𝐼
I(dB) = 10 log ( )
𝐼0
Io – threshold of hearing (human)
- 10-12 w/m2 = 0dB – the lowest hearing threshold
Ex 1: If the intensity of a persons voice is 10-7 W/m2, What is the intensity
level of sound?

2. What is the intensity of a sound wave whose intensity level is 60dB?

3. With one violin playing, the sound level at a certain place is measured as 50
dB. If four violins play equally loudly, what will the sound level most likely
be at this place?(56dB)
 Loudness of Sound in Decibels
Sound Loudness (dbs) Hearing Damage
Average Home 40-50
Loud Music 90-100 After long
exposure
Rock Concert 115-120 Progressive
Jet Engine 120-170 Pain

Home work
1. Two sound waves have intensities of 0.5 W/m2 and 10 W/m2,
respectively. How many decibel is one louder than the other?
2. A man stands at a certain distance from a wall and sets up a simple
pendulum which makes three vibrations per second. He claps his hands
and hears the echo exactly after five complete vibrations of the
pendulum. If the velocity of sound in air is 350m/s, calculate the distance
between the man and the wall?
 Property of sound

https://www.youtube.com/watch?v=uvcvM5ujWJk
http://www.animations.physics.unsw.edu.au/jw/sound-pitch-loudness-timbre.htm
 Resonance of Sound
Resonance is when the frequencies of forced vibrations on an object matches the
object's natural frequency, causing a dramatic increase in amplitude.
Resonance occurs when a source other than the resonating device vibrates at the
exact resonant sound of the said device.
Objects, charged particles, and mechanical systems usually have a certain
frequency at which they tend to vibrate. This is called their resonant frequency, or
their natural frequency.

When a sound or light wave strikes an object, it is already vibrating at some

particular frequency. If that frequency happens to match the resonant frequency of
the object it's hitting, then you'll get what's called resonance. Resonance occurs
when the amplitude of an object's oscillations are increased by the matching
vibrations of another object.
 Standing waves
A standing wave is a wave that remains in a constant position as a result
of interference between two waves traveling in opposite directions.
Consider a wave is set up in the string which is fixed at the two ends. The
wave will travel in both direction and will be reflected at each end.
•
Exercise 1. A standing wave is produced along a string of 120 cm whose
ends are fixed. What is the wavelength of the wave if there are 2 nodes
between the fixed ends of the string?

2. The 4m string tied at one end and the other end is connected to the
vibrator. When the vibrator is vibrated, the string formed a stationary
wave, as shown in the figure below.
 Standing sound waves
Standing waves is caused by reflection at boundaries.
Similar to standing sound waves on the string there is boundary
conditions for sound waves at either side of the medium.
For sound there are two major types of boundary conditions.
1. Open boundary condition- air inside the medium is open to the
atmosphere.
2. Closed boundary conditions- air is blocked to the atmosphere
http://www.acs.psu.edu/drussell/Demos/StandingWaves/StandingWaves.html
 1. Pipe open at both ends
At each open end, the column of air inside the pipe communicates with the
out side air, so the pressure at the ends can’t deviate much from the
atmospheric pressure.
Therefore the open ends are Pressure nodes. Eg: flute

Fundamental Frequency
First Harmonics

Second Harmonics
•

Third Harmonics
•
•
 Homework
2. An organ pipe that is open at both ends has a fundamental frequency of
382 Hz at 200C. What is the length of the organ pipe?

NOTE: Pressure nodes is a displacement antinodes and pressure antinode is a

displacement node.
 2. Pipe open at one end
At the closed boundary the pressure in the pipe is separated from the
atmosphere.
The air at the closed end meets a rigid surface, so there is no restriction
on how far the pressure can deviate from atmospheric pressure. So the
closed end is a pressure antinode. Eg: Trumpet
•
•
Ex 1: The speed of sound waves in air is found to be 340m/s. Determine the
fundamental frequency of a closed end air column which has a length of 67.5
cm.

2. A closed end organ pipe is used to produce a mixture of sounds. The third
and fifth harmonics in the mixture have frequencies of 1100 Hz and 1833 Hz
respectively. What is the frequency of the first harmonic played by the organ
pipe.

https://www.youtube.com/watch?v=N5Ch2NThFvY
Homework
1. The three lowest resonant frequencies of a system are 50Hz, 150Hz,
and 250Hz. The system could be
a. a tube of air open at both ends
b. a tube of air closed at one end.

2. The fundamental frequency of a pipe closed at one end is f1. How

many nodes are present in a standing wave of frequency 9f1.
3. The length of a pipe closed at one end is L. In the standing wave
whose frequency is 7 times the fundamental frequency, what is the
closest distance between nodes?

4. An organ pipe that is open at both ends has a fundamental frequency of

382 Hz at 00C. What is the fundamental frequency of this pipe at 200C?
 Doppler Effect
The Doppler Effect is the change in frequency or pitch that you hear
from a moving source. It will be either higher or lower than the
emitted frequency, depending on the direction the moving source.

https://www.youtube.com/watch?v=h4OnBYrbCjY
 MOVING SOURCE
• When the source is moving at velocity Vs towards a stationary observer on the
right the wavelength –distance between crests is smaller in front of the source
and larger behind the source.
• Let Vs –velocity of source VsTs

Vw – velocity of wave λ

fs – frequency of source
Ts – period of source
VwTs

Consider first the source emit wave crest 1 and then after a period Ts the
second wave crest is emitted ,during this time the source already reach at
point 2.
• Thus the distance between the two crest is wavelength λ.
• Distance travelled by crest 1 is Vw Ts
• During the same time interval, the source travel a distance VsTs
Wavelength λ = Vw Ts – VsTs =(Vw - Vs)Ts
• f0-The frequency at which the crests arrive at the observer is the observed wave
frequency.
• T0- The observed period between the arrival of two crests is the time it takes
sound to travel a distance (Vw - Vs)Ts
𝜆 (𝑉𝑤 − 𝑉𝑠)
𝑇𝑜 = = 𝑇𝑠
𝑉𝑤 𝑉𝑤
• The observed frequency is:
1 𝑉𝑤
• fo = f o= ( ) fs
𝑇0 𝑉𝑤 −𝑉𝑠

• Divide both by Vw
1
• 𝑓𝑜 = 𝑓𝑠
1−𝑉𝑠 𝑉𝑤
• If the source moves in opposite direction to the wave (away from the
source) Vw becomes –Ve.
Exercise 1. If a vehicle is coming toward you at 27 m/s and the sound its horn that
blares at 8000 Hz, what is the frequency of sound you hear when the speed of
sound is 340 m/s?

2. A car moving at a speed of 20m/s produces a sound wave of frequency 500Hz.

Find the observed frequency of a listener standing at the side of the road,
a) if the car is moving towards the listener.

b) If the car is moving away from the listener.

3. A train approaches and passes a platform at a steady speed of 30m/s whistle
sounding its whistle at a frequency of 500Hz. What is the frequency of the
whistle as heard by someone standing on the platform? (speed of sound =
330m/s)
a) As the train approach

b) As the train depart

 Moving observer
• When we consider the observer moving away from the source (in the direction
of wave) and stationary source the Doppler Effect equation become:
𝐕𝐨
𝐟𝐨 = 𝟏− 𝐟𝐬
𝐕𝐰
• fo – observed frequency
• Vo – observer speed
• Vw – wave speed
• fs – frequency of source
Ex 1. A fixed source emits sound of frequency 1000 Hz. What is the
frequency as heard by an observer
(i) at rest
(ii) Moving away from the source at a constant speed of 20 ms-1 and
(iii) Moving towards the source at the same rate.
2. A listener moving at a velocity of 40m/s hears a sound wave of
frequency 340 Hz from a stationary source. Find the frequency of sound
heard by the listener if he is moving
a) Towards the source

b) Away from the source

(take speed of sound as 340m/s)

 Motion of both Source and observer
• If both source and observer are moving, we combine the two Doppler
shifts

1−𝑉𝑜 𝑉 𝑉𝑤 −𝑉𝑜
fo= ( 𝑉 𝑤)fs = ( ) fs
1− 𝑠 𝑉 𝑉𝑤 −𝑉𝑠
𝑤

• Vw and Vs
 +ve for motion in the direction of propagation
 - ve for motion opposite the direction of propagation
Exercise 1: A source and listener are moving towards each other with the speed of
40 ms-1. If the true frequency of sound emitted by the source is 1200 Hz, calculate
the observed frequency when both source and listener are moving towards each
other with the velocity of 40ms-1.
Velocity of sound in air = 340 ms-1.

2 . A source of sound waves of frequency 1kHz is travelling through the air at 0.5
times the speed of sound .
A. Find the frequency of sound received by a stationary observer if the source
moves towards her.
B. Repeat if the source moves away from her instead
3. A source and an observer are each travelling at 280m/s. The source
emits waves at 1kHz. Find the observed frequency if A) the source and
the observer are moving towards each other . B) the source and the
observer are moving away from each other. C) the source and observer
are moving each other.
Velocity of wave is 340m/s
 Ultrasound
• Ultrasounds are sound waves with frequencies higher than the upper
audible limit of human hearing.
• Ultrasound devices operate with frequencies from 20 kHz up to several
gigahertz.
• Ultrasound is used in many different fields. Ultrasonic devices are used
to detect objects and measure distances.
• Ultrasound imaging or sonography is often in medicine. In the
nondestructive testing of products and structures, ultrasound is used to
detect invisible flaws. Industrially, ultrasound is used for cleaning,
mixing, and to accelerate chemical processes.
• Animals such as bats and porpoises use ultrasound for locating prey
and obstacles.
1. It is mostly used in medicine to view the internal organs of the body especially
the developing fetus, measuring blood flow through the heart and major blood
vessels and detecting prostate cancer.
2. It is used in sonar devices to detect the presence of objects underwater. Hence it
is used by submarines, scuba divers and fishing trawlers who use it to detect shoals
of fish.
3. It is used in security systems to detect even the slightest movement in a specified
area.
4.Ultrasound is used in industry to analyze the uniformity and purity of liquids and
solids by means of acoustic microscopy.
5. It is used in humidifiers in which ultrasound waves vibrate a metal sheet to spray
the water as a fine mist.
6. Ultrasonic welding is used to create heat to weld plastics.
7. Ultrasonic cleaning is useful to clean delicate articles of jewelry, watches, and
lenses.