# Intro to waves & speed

```A WAVE IS A
DISTURBANCE THAT
CARRIES ENERGY
THROUGH MATTER OR
SPACE.
Waves
LONGITUDINAL WAVE - Particles vibrate parallel
to the direction of the wave.
LONGITUDINAL:
Transverse & Longitudinal Wave Animation:
Transverse:
TRANSVERSE:
Longitudinal:
TRANSVERSE WAVE - Particles vibrate
perpendicular to the direction of the wave.
Defining Terms
•Amplitude (A): maximum displacement from
equilibrium.
•Period (T): time it takes to execute a
complete cycle of motion
•Frequency (f): number of cycles or vibrations
per unit of time
* Unit: Hz = sec-1
Defining Terms
• Medium: material through which a
disturbance travels.
• Mechanical wave: a wave whose
propagation requires a medium.
• Non-mechanical wave: a wave whose
propagation does not require a medium.
1
Defining Terms
WAVE ANATOMY
TRANSVERSE:
LONGITUDINAL:
Sound wave
(LONGITUDINAL):
Sound Waves
• Mechanical Waves (require a medium)
• Longitudinal waves
• Formed by a series of compressions and
rarefactions.
Frequencies of Sounds
Increasing
Frequency
• Wave Pulse: a single non-periodic disturbance.
• Periodic wave: a wave whose source is some
form of periodic motion.
• Standing wave: wave pattern that results
when two waves of the same f, , and A travel
in opposite directions and interfere.
Infrasonic Sound
(elephants can hear)
f < 20 Hz
Audible Sounds
(humans can hear)
20 – 20,000 Hz
Ultrasonic Sound
(dolphins can
detect)
f > 20,000 Hz
2
Pitch
• How high or low we perceive a sound to be,
depending on the frequency of the sound
wave.
• As the frequency of a sound increases, the
pitch of that sound increases.
Which graph represent the sound with the
highest pitch?
A
C
What is wrong with
these graphs
representing sound
waves?
Sound is
longitudinal, not
transverse.
B
C
Ultrasound
• Images produced by ultrasonic sound show
more detail then those produced by lower
frequencies.
• Ultrasonic sound has many applications in the
field of medicine.
• Ultrasound images, such
as the one shown here, are
formed with reflected sound
waves.
Practice
Amplitude
• Draw a loud and high pitched wave.
• The amplitude of a sound wave corresponds
with how loud the sound is.
– A large amplitude is a loud sound.
– A small amplitude is a quiet sound.
• Draw a loud and low pitched wave.
• Draw a quiet sound wave with medium pitch
Calculating Wave speed:
x 

  f
t T
– V = wave velocity
• Where:
–  = wavelength (m)
– f = frequency (Hz or sec-1)
– T = Period
 (sec)
f 
1
T

v
f
Sample Calculation 1
• A tuning fork produces a sound with a frequency
of 256 Hz. The speed of sound in water is 1500
m/s. Calculate the wavelength produced by this
tuning fork in water.
Given:
f = 256 Hz
v = 1500 m/s
=?

v 1500m / s

256 sec 1
f
 = 5.9 m

3
Wave speeds
• The speed of a wave depends on it’s medium.
• For a wave on a string. The speed of the wave
depends on
– the tension in the string (F).
– the linear density of the string (the mass of string per
unit length) ()
 
mass(kg)
length (m)

F

Example: A cord of mass 0.65 kg is stretched between two
supports 8.0 m apart. If the tension in the cord is 120 N, how long
will it take for a pulse to travel from one support to the other?
m = 0.65 kg
0.65kg

 0.08125 kg
m
8.0m
L = 8.0 m
120 N
F = 120 N v  F 
 38.43m / s

0.08125kg / m
t=?
d
v   t  d  8.0m  8.0m
 0.21sec
38.43m / s
t
v
v

Speed of sound depends on medium and
temperature.
Medium
Gas: air
(0oC)
331
Gas: air (25oC)
Gas: air
V (m/s)
(100oC)
346
366
Liquid: water
(25oC)
1490
Solid: copper
(density = 8.96g/cm 3)
3560
Solid: aluminum
5100
(density = 2.70g/cm3)
Source: Serway/Faughn, p. 461 (Table 14.1)
To calculate the speed of sound through air at
different temperatures…
vsound  (331m / s)
T
273K
331 m/s is the speed of sound at 0oC

T = temperature in Kelvin
Remember: Kelvin = oC + 273
4
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