Ch. 17 Notes – Mechanical Waves and Sound
We encounter waves all the time; some we can hear (sound), some we can see (water waves, visible light), and some we can’t (radio waves, ultraviolet rays). All waves are energy, but not all waves are the same.
mechanical wave – a disturbance in matter that carries energy from one place to another.
ex. Sound waves, water waves, earthquake waves
medium – the material through which a wave travels
• mechanical waves require a medium (matter) to travel through.
• A mechanical wave is created when a source of energy causes a vibration to travel through a medium
• Energy is the ability to do work – we often can see/feel the effects of waves doing work.
There are three main types of mechanical waves: transverse, longitudinal, and surface waves.
transverse wave – a wave that causes the medium to move at right angles (perpendicular) to the direction
in which the wave travels.
• When a transverse wave travels through a medium, the
waves energy causes the medium to vibrate from its rest
position, but it is the energy that travels from one place to
another. The medium vibrates back and forth about a
fixed position as the energy disturbs the matter.
crest – the highest point of the wave above the rest position
trough – the lowest point of a wave below the rest position
In the picture to the right, to create the wave you would shake the
rope up and down. Notice that the wave (the energy) is moving
from left to right as the rope is moving up and down.
longitudinal wave – a wave in which the vibration of the medium is in the same direction (parallel) to the
direction the wave travels
• When a longitudinal wave travels through a medium, the
waves energy also causes the medium to vibrate from
its rest position as the energy travels through the medium.
The difference in a longitudinal wave is that the medium
vibrates in the same direction as the wave is traveling
compression – the area where the particles in the medium
are spaced close together (comparable to the crest)
rarefaction – the are where the particles in the medium are
spread apart (comparable to the trough)
In the picture to the right, to create the wave, you would push
or pull the end of the spring. As the energy travels through the spring, it causes some of the coils to be pushed closer together than they were in the rest position (compression). As the compression moves to the right, the coils behind it are spread out more than they were in the rest position (rarefaction).
surface waves – a wave that travels along a surface separating two media.
A surface wave combines the motion of a transverse and a longitudinal wave
• the most familiar type of surface wave we encounter occurs in water. As
the water wave travels on the surface of the water (the boundary between
the water and the air) the water carries the energy of the wave from left to right.
When a crest passes an object in the water, the object moves up, and when a
trough passes, the object moves down. However, the object is also pushed
back and forth by the surface wave (like the motion of a longitudinal wave).
The combination of these two motions causes the object to move in a circle.
In deep water, an object would not move along with the wave; it would move
around a fixed position. As a surface wave approaches shallow water, the
behavior changes as friction between the water and the shore slows down the
bottom of the wave. The top of the wave continues at its original speed, so the wave topples over on itself.
Properties of Mechanical Waves
Most wave motion repeats at regular time intervals – this is called periodic motion (or simple harmonic motion). Waves with periodic motion can be described using properties called period, frequency, wavelength, speed and amplitude.
period (T) - the time required for one cycle (one complete motion returning to its starting point).
- often the easiest way to measure period is the time between two successive crests (or compressions)
frequency (f) – the number of complete cycles in a given time (usually 1 second).
- frequency is measured in cycles per second, or hertz (Hz).
• Frequency and period are inversely related. T = 1/f or f = 1/ T
- A wave with a frequency of 4 Hz has a period of ¼ seconds.
- A wave with a period of 4 seconds has a frequency of ¼ Hz.
• A waves frequency equals the frequency of the vibrating source producing the wave.
- if you shake the end of the rope up and down two times per second, the wave traveling through the rope will have a
frequency of 2 Hz, and a period of ½ seconds (which means it took ½ of a second for one cycle to occur). If you
shake it up and down 3 times per second, the frequency will be 3 Hz, and the period will be 1/3 seconds.
wavelength () – distance between a point on one wave and the same point
on the next cycle of the wave.
- wavelength is usually measured between adjacent crests or adjacent
troughs (or adjacent compressions/rarefactions)
• frequency and wavelength are inversely related - increasing the frequency
of a wave decreases its wavelength and decreasing the frequency
increases the wavelength (and vice-versa). Assuming the two waves
in the picture to the right are traveling at the same speed, since wave B
has a shorter wavelength, it will have a higher frequency (more waves
will pass by each second)
amplitude – the maximum displacement of the medium from its rest position
- the amplitude of a transverse wave is the distance from the rest
position to a crest (or a trough).
- the amplitude of a longitudinal wave is the maximum displacement
of a point from its rest position (maximum compression)
• the more energy a wave has the greater its amplitude – it takes more energy
to produce a wave with higher crests and deeper troughs (or greater
compressions and rarefactions).
wave speed – the speed at which a wave is moving.
We know that speed is distance divided by time. For waves, distance is measured by wavelength and time is measured by period, so we can find wave speed by dividing wavelength by period. However, since frequency is a more commonly used property (and is the inverse of period), we alter the formula:
wave speed = frequency • wavelength
( m/s = Hz • m )
Ex 1: A wave on a rope has a wavelength of 2.0 m and a Ex 2: If a sound wave travels at 330 m/s, what is the
frequency of 2.0 Hz. What is the speed of the wave? wavelength of a 280 Hz note?
Given Formula Solution Given Formula Solution
Behavior of Waves
When waves interact with each other or encounter a different medium, they can have different behaviors or interactions that we can describe as reflection, refraction, diffraction and interference.
reflection - the interaction that occurs when a wave bounces off a surface that it cannot pass through
• If you send a wave down a rope that is attached to a wall, the wave reflects when it hits the wall.
• Reflection does not change the speed or the frequency of a wave, but it can change the phase of the
wave – depending on the firmness (or rigidity) of the new medium, the wave may flip upside down.
refraction – the bending of a wave as it enters a new medium at an angle
• When a wave enters a medium at an angle, refraction occurs because one
side of the wave moves more slowly than the other side (see pictures on pg. 509).
• If the wave front is parallel to the boundary of the new medium, the wave will change speed, but will not
change direction. This is because all parts of the wave change speed
equally at the same time.
diffraction – the bending of a wave as it moves around an obstacle or passes through a narrow opening
• As a wave passes through a narrow opening, the wave will
spread out – changing direction.
• As a wave passes around the edge of an obstacle, the wave will
bend a little – changing direction.
• A wave diffracts more if its wavelength is large compared to the size
of the opening or obstacle
interference – the interaction that occurs when two or more waves overlap and combine together
• unlike particles, waves can occupy the same region of space at
the same time and then continue on.
constructive interference – when two or more waves combine
to produce a wave with larger amplitude
destructive interference - when two or more waves combine
to produce a wave with smaller amplitude
At certain frequencies, interference between waves can produce a standing wave.
standing wave – a wave that appears to stay in one place – it does not appear to move through the medium
node – a point on a standing wave that has no displacement from the rest position
- a node is the result of complete destructive interference between the waves
antinode – a point between two nodes that has maximum displacement from the rest position
- an antinode is the result of complete constructive interference between the waves
Sound and Hearing
Sound waves are longitudinal waves. Many behaviors of sound can be explained using a few properties:
speed – the speed that sound waves travel depends on the medium. In dry 20°C air, sound travels at 342 m/s
• the speed of sound depends on factors such as the density and elasticity of the medium
intensity – corresponds to the energy of a sound wave, which depends on the amplitude and the distance from the source. Intensity is measured in decibels (dB).
• The decibel scale is logarithmic – it is based on powers of 10. A 0 dB sound can barely be heard. A 20 dB sound is 100 times more intense (has 100 times the energy) and a 30 dBis 1000 times more intense.
loudness – is the physical response to the intensity of sound. It is subjective (depends on a persons interpretation)
pitch – corresponds to the perception of the frequency of a sound.
• High frequency sounds have a high pitch and low frequency sounds have a low pitch
• Instruments produce standing waves of different frequencies. Long standing waves have a longer
wavelength lower frequency which we perceive as a lower pitch.
Doppler effect – a change in frequency caused by the motion of the source
of a sound, motion of the listener, or both
• As a source of a sound moves closer, the wave fronts bunch together causing
a shorter wavelength and a higher frequency – we hear a higher pitch.
• As the source moves away, the wave fronts spread apart causing a longer
wavelength and a lower frequency – we hear a lower pitch.
Hearing and the Ear
Our ears gather and focus the vibrations of sound waves, and then convert
those vibrations into signals which are sent to the brain and interpreted.
Outer ear -Your ear funnels sound waves down the ear canal where they strike the eardrum
(a tightly stretched membrane), vibrating it at the same frequency as the sound waves
Middle ear – contains 3 tiny bones (hammer, anvil and stirrup) which the eardrum causes to
vibrate at the same frequency. The three bones act as a lever system, amplifying the sound
Inner ear – vibrations from the stirrup travel into the cochlea, a tiny spiral shaped canal filled
with fluid lined with thousands of tiny hair-like nerves. As these hairs vibrate they send
signals to your brain, which your brain interprets the signals as sound.
Modern sound equipment has a similar process converting sound waves into electronic signals to record sound, or converting electronic signals back into sound waves produced by speakers.