1. Much of what we need to know about waves can be found by observing
water waves. In doing so, we find two major features of all waves:
(a) a wave is a traveling disturbance, and (b) a wave carries energy from
place to place.
2. Wave motion also has properties of SHM since wave particles vibrate
around an equilibrium position as the wave travels.
3. There are three kinds of waves: transverse, longitudinal, and surface
waves. These are based on the movement of wave particles relative to the
4. For a transverse wave, vibrations are perpendicular to wave velocity. In a
longitudinal wave, vibrations are parallel to wave velocity. For the third kind,
surface waves (also called water waves), particles move both perpendicular
and parallel to the direction of the wave's motion.
5. Transverse and longitudinal waves are also called periodic waves because
they consist of cycles or patterns that are produced over and over again by
6. The terms that the study of waves share with SHM are cycle, amplitude,
period, and frequency.
7. Mechanical waves, such as sound waves or waves on a rope, for example
require a medium. Electromagnetic waves, such as light and radio waves, do
not need a medium.
8. Waves transfer energy, either by mechanical or electromagnetic means,
without the transfer of matter.
9. The shortest distance between points where the wave pattern starts to
repeat itself is called the wavelength, and is indicated by the Greek letter,
10. A wave disturbance moves in straight lines in all directions away from the
source (rectilinear propagation). This allows us to use the distance-rate-time
equation d = v·t .
11. The frequency ( in sec.-1 or Hertz, Hz.) of a wave, given by f, is the
number of vibrations per second of any one point on a wave.
12. Period, the reciprocal of frequency, T = 1/f , is the time for a wave to
13. The velocity of a wave, the distance a point on a wave moves in a unit
time interval can be calculated using the wave equation, v = f·λ.
14. The amplitude of a wave is the maximum displacement from the
15. The highest point above the equilibrium position is called the crest, and
the lowest point below is called the trough.
16. Energy transferred by a wave is proportional to the square of the
17. The speed of a wave depends on the properties of the medium through
which it travels. Research dealing with waves carried by a string produced
the equation v = √(F/µ), where F is the tension in the string, and µ is the
mass per unit length, µ = m/L.
18. If two or more waves are moving through a medium, the resultant wave
is found by adding amplitudes together, point by point. This is known as the
Principle of Superposition.
19. Standing waves are formed when two waves having the same frequency,
amplitude and wavelength, travel in opposite directions in a medium and
20. When waves reach a boundary between two media, they are partially
transmitted and reflected. The amount of reflection depends on how much
the two media differ.
21. When a wave moves from a more dense to a less dense medium, the
reflected wave is erect. But in moving from less dense to more dense, the
reflected wave is inverted.
22. Maximum destructive interference produces nodes while maximum
constructive interference produces antinodes.
23. Waves are reflected from a barrier at the same angle, measured against
the normal, as they approach it.
24. The Law of Reflection states that the angle of incidence equals the
angle of reflection, m ⁄ (i) = m ⁄ (r) .
25. The spreading of waves around the edge of a barrier is known as
diffraction. While the change in direction of waves at the boundary of
two different media is known as refraction.
26. Sound, produced by vibrating objects, is a longitudinal wave
transmitted through a gas, liquid, or solid. For sound, instead of crest
and trough, we use the terms condensation and rarefaction.
27. A sound wave is an oscillation in the pressure of the medium, with
the ear and brain perceiving the amplitude as loudness or intensity, or
I = P/(4πr2).
28. The frequency of a sound wave determines its pitch, and on the
musical scale, two notes that differ by one octave have pitches in ratio
2:1. A sound wave of a single frequency is called a pure tone.
29. For most humans, the sonic spectrum consists of frequencies between
20 Hz and 20 kHz. Infrasound is <20 Hz., while ultrasound is >20 kHz.
30. The Doppler shift is the change in frequency of a sound caused by motion
of either the source, s, or observer, o. The apparent frequency can be
calculated using the equation, fo = fs·((v +/– vo)/(v –/+ vs)).
31. The amplitude of a sound wave is measured on a scale of decibels (dB),
with β=(10 dB)·log(I/Io). The threshold of hearing is, Io = 1.0x10-12W/m2.
32. The speed of sound in air at 0.0oC is 331.5 m/s, and increases by .60 m/s
per degree rise in air temperature. Speed depends on medium.
33. In an Ideal Gas the speed of sound is given by v =√(γkT/m), where
γ = cp/cv, k is Boltzmann's constant, T is the Kelvin temperature, and m is
the mass of a molecule of the gas.
34. In a liquid v =√(Bad/ρ), where Bad is the adiabatic bulk modulus, and
ρ is the mass density. For a solid (long slender bar) we have, v =√(Υ/ρ),
where Υ, the Greek letter upsilon, is Young's modulus.
37. Most sounds consist of waves with more than one frequency with the
quality of the wave called timbre.
and still, we need these steps to solve any problem in Physics:
(i) read the problem and identify the given variables
(ii) determine what you are asked to solve for
(iii) find the correct equation to use
(iv) use Algebra, Trigonometry, and/or Calculus to isolate the unknown
(v) substitute-in the given information and simplify.
Problem Set #1 on Waves. Click HERE.
Problem Set #2 on Waves. Click HERE.
For the Speed of Sound Lab Handout. Click HERE.
For the Lab Abstract template. Click HERE.