3. How does sound move through air?
Air particles get pushed by a force (e.g. our voice, or a guitar string vibrating)
The air particles bump against each other, and vibrate back and forth
Eventually, this vibration of particles reaches our ears, and makes our eardrums vibrate –
our brains then interpret this as sound
If we were to look at the air between the source of the sound and our ears, we would see
areas where particles are more bunched together, and areas where they are more
spread apart
We call this a sound wave
4. Sound
Waves
• Individual particles move side to side
• The vibration moves through the
particles
• Image is from here:
https://www.acs.psu.edu/drussell/Dem
os/waves-intro/waves-intro.html
5. Sound wave
propagation
• Individual particles move side to side
• The vibration moves through the
particles
• Image is from here:
https://www.acs.psu.edu/drussell/Dem
os/waves-intro/waves-intro.html
6. Measuring Sound Waves
To start with, particles are randomly
distributed
When the force (voice, guitar string,
speaker) starts moving them, some get
squashed closer together, others pulled
further apart
In the squashed together bits we get
higher pressure, in the pulled apart bits we
get lower pressure
7. Measuring
Sound
Waves –
wavelength,
frequency,
velocity
• Wavelength ( ) – distance between two points
ƛ
at the same level (two peaks, two troughs, two
zeroes)
• Frequency (f) – number of times per second a
point moves from peak to trough and back
again
• Velocity (v) – speed at which the disturbance
(sound) moves through the medium (e.g. air)
• These three are related by a basic equation
v = f ƛ
(velocity = frequency x wavelength)
8. Example of v = f ƛ
A wave has a frequency of 100 Hertz (100Hz) – this means any point on the wave moves
up and down 100 times every second
The same wave has a wavelength of 2 metres (2m) – so every time a point moves up and
down again, the disturbance moves 2m
The velocity of the disturbance is 200 metres every second - 200m/s or 200ms-1
The wave goes up and down 100 times every second, and each time it moves 2m
v = f = 100 x 2 = 200ms
ƛ -1
9. Sound waves in air
In air at around 20 the velocity of sound waves is about 344ms
℃ -1
In water, sound moves faster at around 1,481ms-1
, and in iron it is even faster at 5,120ms-1
This is because in liquids and solids the particles are packed closer together, so the vibrations pass more easily
between them
So, for calculations about wavelength and velocity in air, we can always use v = 344ms-1
If we want to calculate frequency, we use f = v/ ƛ
If we want to calculate wavelength, we use = v/f
ƛ
This means, in air, any given frequency always converts to a single wavelength and vice versa
Higher frequency means shorter wavelength, lower frequency means longer wavelength
Frequency is what we perceive as pitch in musical notes
Why we usually need bigger speakers for bass – longer wavelength needs a bigger enclosure
Why a ukulele produces higher notes than a guitar – shorter string, shorter wavelength, higher frequency
10. Examples of soundwaves in air
Middle C (C4) has a frequency of around 262Hz – what is its wavelength in air?
= v/f = 344/262 = 1.3m
ƛ
A sound wave in air is measured to have a wavelength of 78cm, what is its frequency?
F = v/ = 344/0.78 = 441Hz (this is roughly A
ƛ 4)
A note has a wavelength in air of 60cm, what is its frequency?
A note has a frequency of 1,760Hz, what is its wavelength in air?
11. Measuring
sound waves
– Loudness,
pressure and
intensity
As well as pitch (which relates to
frequency/wavelength), we are also going to
be interested in loudness
This is more challenging because loudness is
subjective (it depends on the listener)
If we do experiments, it’s difficult to get
people to agree on where a particular sound
lies on, e.g., a scale of 1-10
What’s much more consistent is people
agreeing when a sound gets louder/quieter
by a certain amount (e.g. twice as loud/quiet)
Thankfully, experiments show that this is closely
related to changes in the sound pressure (the
squishing together of air particles), which is
something we can measure
12. Sound pressure
Pressure is a measure of the force (e.g. weight) applied over an area
If you squeeze a balloon between the palms of your hands, it’s unlikely to burst – because the force is
spread over a large area, so the pressure is low
If you touch the balloon even quite gently with a pin, it’ll probably burst – because the force is
spread over a tiny area (the tip of the pin), so the pressure is very high
In equation terms we write that Pressure = Force / Area, or P = F/A
Force is measured in Newtons (after Isaac) - N
Area is measured in metres squared (metres x metres) – m2
So, P = F/A = N/m2, which can also be written as Nm-2 (both read as ‘Newtons per metre squared’)
Pressure as a concept was first written about by a French scientist called Blaise Pascal, so we
use units called ‘Pascals’ (Pa) for it – 1Pa is the same as 1Nm-2
13. Sound pressure and human hearing
The smallest change in sound pressure that can generally be heard by humans is 20 µPa (20
micro-Pascals)
This is 20 x 10-6
Pa, or Pa, or 0.00002 Pa
Equivalent to a leaf rustling, or calm breathing
At the other end of the scale, the threshold at which a change in sound pressure can be painful
can be anywhere from 20 – 200 Pa (very individual dependent)
Equivalent to a jet engine
Between 1 million and 10 million times higher than the smallest audible change
We don’t really want to use a scale from 0.00002 to 200 to measure the sounds that humans can
hear – it’s too large and a bit messy (lots of decimal points and zeros)
So, we use a trick called logarithms to compress this scale to something that’s more manageable
