This document outlines key topics in waves and physics, including: 1) Pulses in a string, principle of superposition, periodic waves, types of waves like transverse and longitudinal, and standing waves. 2) Sound waves are mechanical waves that propagate through elastic media like solids, liquids, and gases. The speed of sound and waveforms of different musical sounds are discussed. 3) Interference of sound waves, including beats produced by waves with slightly different frequencies. The Doppler effect of changing sound frequency due to relative motion of source and listener is also covered.

1. Waves
Physics 2

2. Topic Outline
• Pulses in a string
• Principle of Superposition
• Periodic Waves
• Types of Waves
• Standing Waves
• Sound
• Interference of Sound Waves
• Doppler Effect
• Sound Intensity

3. Pulses in a String

4. Example:

5. Reflection at a Boundary

6. Reflection and Transmission at a
Junction

7. Principle of Superposition
When two pulses travel past a point in a string at the same time, the
displacement of the string at that point is the sum of the sum of the
displacement each pulse would produce there by itself.

8. Periodic Waves

9. Three quantities used to describe
waves
This formula applies to all periodic waves,
sinusoidal or not.

10. Example:

11. Period
Period T of a wave is the time required for one
complete wave to pass a given point.

12. Example:

13. Amplitude
The Amplitude A of a wave refers to the
maximum displacement from their normal
positions of the particles that oscillate back and
forth as the wave travels by.

14. Fourier’s Theorem
A theorem by Jean
Fourier (1768 – 1830)
shows that any
periodic wave of
frequency f,
regardless of its
waveform, can be
thought of as a
superposition of
sinusoidal waves
whose frequencies are
f, 2f, 3f and so on.

15. Types of Waves
Waves may be transverse, longitudinal,
or a combination of both.
Waves in stretched string are transverse
waves because the individual segments
of the string vibrate perpendicular to the
directions in which the waves travel.
Longitudinal waves occur when the
individual particles travel back and forth
parallel to the direction in which the
waves travel.
Waves in the body of water (or other
liquid) are combination of transverse
and longitudinal waves. Each molecules
moves in a circle with a period equal to
period of the wave.

16. Standing Waves
Standing waves are results of
waves that travel down the string
in both directions, are reflected at
the ends, proceed across to the
opposite ends and are again
reflected, and so on.
Interference is the interaction of
different wave trains.
Constructive interference occurs
when the resulting composite
wave has an amplitude greater
than that of either the original
waves, and destructive
interference occurs when the
resulting composite wave has an
amplitude less than that of either
of the original waves.

17. Fundamental Frequency, Overtones,
and Harmonics

18. Example:

19. Resonance
Resonance is the response of an oscillator
when a driving force is applied to an
oscillating system at a frequency near the
natural frequency of the system, the
amplitude of the oscillation becomes large.

20. Sound Waves
An acoustic wave is any mechanical wave that
propagates through an elastic medium, which may be
solid, liquid or gaseous.
Sound wave is the term used to refer to mechanical
waves, usually in air, having a frequency within the
range of human hearing, about 20 Hz to 20 kHz.
Infrasonic waves are those having frequency less than
20 Hz and ultrasonic waves for those frequency
greater than 20 kHz.

21. Speed of Sound

22. Waveforms of Some Musical Sounds

23. Beats
Beats are the loudness pulsations of a sound.
The origin of bits in sound waves Beats produced by waves whose frequencies differ by 5%

24. Doppler Effect
Doppler Effect is the change in frequency of a sound brought
about by relative motion between source and listener.

25. Sound Intensity Level

26. REFERENCE:
Modern Technical Physics 6th Edition by Arthur
Beiser
Copyright © 1992 by Addison‐Wesley Publishing
Company, Inc.
Physics for Students of Science and Engineering
by A.L. Stanford and J.M. Tanner
Copyright © 1985 by Academic Press, Inc.