Waves can be characterized by their wavelength, amplitude, frequency, and period. The wavelength is the distance between matching portions of two waves, amplitude is the height of the wave, frequency is the number of waves per second, and period is the time for one full cycle. The relationship between frequency and period is that frequency equals 1 divided by period, and period equals 1 divided by frequency. When a wave passes through a medium, the medium itself does not move but rather gets displaced in an up and down or side to side motion depending on if it is a longitudinal or transverse wave.

1. Waves

2. • Wavelength
– The distance between matching portions of two waves.
• Amplitude
– The height above the midpoint of the wave.
• Frequency
– The number of waves occurring each second.
• Period
– The time required to complete one cycle
Naming stuff for waves:

3. Relationship between frequency and
period
• Frequency = 1/period
• Period = 1/frequency
Example Problem:
Gusts of wind cause the Sears Building in Chicago to
sway back and forth completing a cycle every 10
seconds.
a) What is the period?
b) What is the frequency?

4. Example problem
• Identify the following:
– period
– amplitude
• Calculate:
– frequency
-4
-3
-2
-1
0
1
2
3
4
0 0.25 0.5 0.75 1 1.25 1.5 1.75 2
Displacement(m)
Time (s)

5. Wave motion
• When a wave passes,
the medium itself does
not move.
– It just gets displaced.
– The blue dot follows the
red circle. Overall it goes
nowhere.
– The speed of sound is
340 m/s. Clearly the air
does not move this fast
(what wind).

6. Wave speed
• The speed of a wave’s motion is related to its
frequency and wavelength:
– velocity = frequency * wavelength
If the wavelength
is 1 m and one
wavelength per
second passes
the pole, then
the speed of the
wave is 1 m/s.

7. Example Problem
• The speed of sound is 340 m/s.
– What is the wavelength of a sound with a frequency
of 220 Hz?
– What is the frequency of a sound with a wavelength
of 10 cm?

8. Transverse and Longitudinal Waves
• Longitudinal waves: waves which move by
compression/rarification.
– Prime example: sound
• Transverse waves: waves which move by lateral vibration.
– Prime example: ocean waves
• Demo!

9. • Recall our description of a gas.
– gas particles may be locally more or less dense, it is easy to move them and compress
them.
• Wavelength of a sound wave is the distance between successive
compressions/rarefactions.
• Human ear can typically hear from about 20 Hz to 20,000 Hz.
– Shrinks as we age.
– Mosquito ring tone
Sound Waves

10. Sound 2
• Any material that can vibrate can transmit
sound.
– air
– liquid (sound travels better in water: sonar)
– solid
• Speakers work by vibrating a cone (using an
electromagnet and a permanent magnet) which
causes nearby air to vibrate.
• (rubens tube)

11. Example Problems
• How does a tuning fork emit sound?
• Why does sound travel faster in warm air?

12. Forced Vibration and Natural
Frequencies
• A vibrating object in contact with another object
will tend to force vibrations in the other object.
• Every elastic object (everything) has its own
set of natural frequencies at which it will
vibrate.
– depends on shape, elasticity, etc.
– Sound of an object when it is struck or falls is
produced, in part, by these frequencies.

13. Resonance
• Good example: pumping your legs on a swing to increase the
amplitude.
– The frequency you swing your legs matches the resonance frequency of
the swing.
• Another example: one tuning fork driving another.

14. Resonance 2
• Resonance may be destructive.
– Shattering a wine glass with sound by driving it at a
natural frequency.
– Bridge collapse (video)
• Example Problem:
– When you listen to a radio, why do you hear only
one station at a time instead of all stations at once?

15. Interference
• Waves may interact with one another.
– At any point their amplitudes may sum.
• If two waves happen to meet when their amplitudes
are peaked you get reinforcement.
• If one wave at its trough of one meets another at its
peak you get cancellation.

16. Beats
• Beats may be familiar to anyone who has tuned a guitar.
– Waves at two frequencies meet.
• Sometimes they meet constructively.
• Sometimes destructively.
• The result is we hear the amplitude of the sound increasing and decreasing.

17. Demo
• Detuned tuning fork and normal tuning fork
form beats.

18. Standing Waves
• When a wave reflects
back on itself you get
standing waves.
• String vibrates up and
down in place.
• Places which do not
move are called nodes.
• Places of maximum
motion are antinodes.

19. Demo: Standing Waves
• There are resonance
frequencies available to
any standing wave.
• fundamental and
following tones.

20. Example Problem
• Distinguish between constructive and destructive
interference.
• Suppose a piano tuner hears three beats per second
when listening to the combined sound from his tuning
fork and the piano note being tuned. After slightly
tightening the string he hears five beats per second.
Should the string be tightened or loosened?