PERIODIC MOTION AND MECHANICAL WAVES AND SOUNDS

• Hooke’s Law – increasing the weight by MECHANICAL WAVES AND SOUNDS

equal amounts increases the stretch of the
• Mechanical waves – a non-physical
spring by equal amount
quantity that travels through a material
⃗⃗⃗
𝐹𝑠 = −𝑘𝑥
𝑘
• Transverse wave – the vibration direction
o IN EQUILIBRIUM, 𝑎 = − ( 𝑚) 𝑥 is perpendicular to the direction of the
𝑘 wave propagation
or 𝑎 = −𝑤 2 𝑥 given that 𝑤 = √𝑚
• Longitudinal wave – vibration direction is
• Simple Harmonic Motion – motion of an parallel to the direction of the wave
oscillating system given that: propagation.
o No net force acts on the system.
o Restoring force is proportional to
the opposite directed to the
displacement.
o Motion is periodic.

• Reflection – the wave is diverted back

T = period into the original medium
• Refraction – The speed of the wave
f = frequency changes due to the different
ω = angular velocity characteristic of the new material.
• Diffraction – bends around an edge of
A = amplitude an object.
• Simple Pendulum – an object attached to • Dispersion – waves of different
a frictionless pivot by a cable with a frequency spreads apart from one
negligible mass. another.
• Interference – two or more waved
𝐹𝜃 = −𝑚𝑔𝑠𝑖𝑛𝜃 overlap in the same region of space.
o For small angles, 𝐹𝜃 = −
𝑚𝑔
𝑥 • Velocity of a wave:
𝐿
𝒗 = 𝝀𝒇
v = velocity of the wave
λ = wavelength
f = frequency
• Velocity of a Transverse wave: • Wavelength for nth harmonic:
2𝐿
𝑇 𝜆=
𝑛
𝑣 = √𝜌 • Frequency for nth harmonic:
𝑣 𝑛𝑣
T = tension 𝑓= =
𝜆 2𝐿
ρ = linear density • Doppler Effect – is the apparent
change in the frequency of a wave
due to the relative motion between
the source and the listener.
• Case # 1 - the source moves and the
observer is at rest.
𝑓𝐿 𝑉
=
𝑓𝑠 𝑉 ± 𝑉𝑠
𝒇𝑳 – frequency observed by the listener
𝒇𝒔 – frequency observed by the source
𝑽 – velocity of the sound in the transmitting
medium
• Nodes – Points of zero amplitudes
𝑽𝒔 – velocity if the source
▪ Destructive
interference Take note: + for away, - for toward
• Antinodes – points of high amplitudes
• Case # 2 – the observer moves and
▪ Constructive
the source is at rest.
interference
• Segments (n) – number of harmonics 𝑓𝐿 𝑉 ± 𝑉𝐿
=
in a standing wave. 𝑓𝑠 𝑉

𝒇𝑳 is the frequency observed by the listener

𝒇𝒔 is the frequency observed by the source
𝑽 is the velocity of sound in the
transmitting medium
𝑽𝑳 is the velocity of the listener
Take note: + for toward, - for away

• Case #3 – both the source and the

listener are in motion
𝑓𝐿 𝑉 ± 𝑉𝐿
=
𝑓𝑠 𝑉 ∓ 𝑉𝑠
 𝒇𝑳 is the frequency observed by the
listener
𝒇𝒔 is the frequency observed by the
source
𝑽 is the velocity of sound in the
transmitting medium
𝑽𝑳 is the velocity of the listener
Take note that: + for toward, - for away for
𝑉 ± 𝑉𝐿 and – for toward, + for away for
𝑉 ∓ 𝑉𝑠 .

• Case # 4 – both the observer and

listener are stationary
𝑓𝐿 = 𝑓𝑠
Given that:
𝑣
𝑓𝑆 =
𝜆

• Pitch – property of sound that is

proportional to the frequency.
o High pitch means high
frequency.
o Low pitch means low
frequency.