Chapter 12: Vibrations and Waves
&
Chapter 13: Sound
Key Terms
Simple harmonic motion – vibration about an equilibrium position in which a restoring force is
proportional to the displacement from equilibrium.
Amplitude – the maximum displacement from equilibrium.
Crest – the highest point above the equilibrium position.
Trough – the lowest point below the equilibrium position.
Wavelength – the distance between two adjacent similar points of the wave, such as from crest to
crest or from trough to trough.
Period – the time it takes to execute a complete cycle of motion.
Frequency – the number of cycles or vibrations per unit of time.
Medium – the material through which a disturbance travels.
Transverse wave – a wave whose particles vibrate perpendicular to the direction of wave motion.
Longitudinal wave – a wave whose particles vibrate parallel to the direction of wave motion.
Constructive interference – interference in which individual displacements on the same side of
the equilibrium position are added together to form the resultant wave.
Destructive interference – interference in which individual displacements on opposite sides of
the equilibrium position are added together to form the resultant wave.
Reflection – the turning back of a wave at the surface of a substance.
Refraction – the bending of a wave disturbance as it passes at an angle from one medium to
another.
Diffraction – the spreading of waves into a region behind an obstruction.
Standing wave – a wave pattern that results when two waves of the same frequency, wavelength,
and amplitude travel in opposite directions and interfere.
Node – a point in a standing wave that always undergoes complete destructive interference and
therefore is stationary.
Antinode – a point in a standing wave, halfway between two nodes, at which the largest
amplitude occurs.
Doppler Effect – a frequency shift that is the result of relative motion between the source of
waves and an observer.
Pitch – the perceived highness or lowness of a sound, depending on the frequency of the sound
waves.
Resonance – a condition that exists when the frequency of a force applied to a system matches
the natural frequency of vibration of the system.
Fundamental frequency – the lowest frequency of vibration of a standing wave.
Harmonic series – a series of frequencies that includes the fundamental frequency and integral
multiples of the fundamental frequency.
Beat – interference of waves of slightly different frequencies traveling in the same direction,
perceived as a variation in loudness.
Key Equations
Hooke’s Law
Felastic=-kx
spring force (N) = -[spring constant (N/m) * displacement (m)]
Period
T=t/cycles
period (s) = time (s) / number of cycles of motion
Frequency
f=cycles/t
period (Hz or sec-1) = number of cycles of motion / time (s)
Inverse Relationship between Period and Frequency
f=1/T or T=1/f
Period of a Simple Pendulum in Simple Harmonic Motion
T=2π√(L/g)
period (s) = 2π * √[length (m) / free-fall acceleration (m/s2)]
Period of a Mass-Spring System in Simple Harmonic Motion
T=2π√(m/k)
period (s) = 2π * √[mass (kg) / spring constant (N/m)]
Speed of a Wave
v=fλ
speed of a wave (m/s) = frequency (Hz) * wavelength (m)
Harmonic Series of Standing Waves
fn=nv/2L
frequency (Hz) = harmonic number * speed of waves (m/s) / [2 * length of string/pipe (m)]
Notes