Sound and Waves
Physics 11, Unit 4
Learning Goals
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Learn about wave characteristics
What type of wave is sound?
What factors affect the speed of sound?
How can we measure the speed of sound experimentally?
Waves
A wave is a way for energy to be transferred from point A to point B. Some
waves require a medium to travel through (like water waves or sound). Water
waves transfer energy from point A to point B because the disturbance of the
water molecules at point A affects the surrounding molecules and this causes a
chain reaction and the energy initiated at point A gets spread out through the
water.
As we know, energy comes in many different forms and the total energy is
always conserved. There are other types of waves that don’t require a medium
like electromagnetic waves (light, microwaves, radio waves, X-rays, etc.).
Electromagnetic waves can travel through the void of space, but sound waves
cannot.
Mechanical Waves
Waves that involve the oscillation of particles in a medium are called mechanical
waves. There are two types of mechanical waves:
1. Transverse Waves - the particles in the medium oscillate perpendicular to
the direction of wave motion. Ex: Water waves
2. Longitudinal Waves - the particles in the medium oscillate parallel to the
direction of wave motion. Ex: Sound waves
You can visualize the difference by taking a slinky and causing a disturbance at
one end in both perpendicular and parallel directions to the slinky.
Dimensions
The waves on the slinky or a wave travelling through a string would be classified
as one-dimensional waves since the energy is carried through the medium in one
direction.
Two-dimensional waves can be visualized as the ripples created in a pond or the
vibrations that travel through the wood floor in the gym when you bounce a
basketball. The energy travels outward from the source and can be visualized as
an expanding circle (like the ripples). The total energy from the source is
distributed along the circumference of the expanding circle.
Three-dimensional waves are like sound waves. The energy travels outward from
the source in the shape of an expanding sphere. The total energy from the
source is distributed over the surface area of the expanding sphere.
Wave Terminology
Crests/Troughs - Parts of the wave that are above and below the equilibrium line
respectively
Wavelength (𝝀) - The distance between successive crests or troughs, measured
in meters
Amplitude - The maximum displacement from equilibrium
Frequency (f) - The number of waves sent from the source per second, measured
in Hertz (Hz)
Period (T) - The time between successive waves from the source, measured in
seconds
Rarefaction - Another word for expansion in the previous image.
Universal Wave Equation
From our definition of Period and Frequency, we can say that
We know that speed is distance divided by time and this applies to waves, but
let’s consider the distance and time between two successive waves produced by
the source.
OR
← Universal Wave Equation
Speed of a wave on a string
The speed of a wave on a string can be affected by the tension (FT) in the string
as well as the linear density (𝝁) of the string. The linear density is the mass per
unit length of the string (𝝁 = mass / length )
If more tension is applied to the string, the wave will travel faster through the
string. If the string is heavier, then the wave will travel slower through the string.
The relationship is stated as:
Phet Interactive Tool
Sound Waves
Sound is a three-dimensional longitudinal wave. A source causes rapid
disturbances in the air molecules which causes compressions and rarefactions
of the air molecules, creating pockets of high pressure and low pressure
travelling outwards in all directions from the source. Our ears are sensitive to
these changes in pressure and we can interpret and distinguish them as sound.
The speed of sound is directly affected by arrangement of the particles in the
medium. Sound in air travels around 340 m/s while sound in water travels
around 1500 m/s.
Sound Waves
In fact, the temperature (T ℃) of air affects the speed of sound because of the
physical properties of air molecules in cold vs. warm air.
In warm air, the air molecules are naturally vibrating faster than in cold air and so
there are more collisions between air molecules allowing for a faster transfer of
energy from point A to point B.
**There are different variations of the above formula. This one comes from the
textbook Nelson Physics 11 (2011)
Measuring the Speed of Sound
There are different ways of measuring the speed of sound experimentally. One
way is to use the resonance of a half-closed air column and this is discussed
when resonance and standing waves are studied.
Another way is to use echoes. For an echo to be audible, there needs to be a
large flat surface at some considerable distance away from the source that will
“reflect” the sound wave. If we can find the time it takes for an echo to be heard
and the distance between the source and the wall, we can calculate the speed of
sound simply by using speed = distance / time. Don’t forget that the sound wave
has to travel to the wall and back in order for you to hear an echo.
Human Hearing
Humans, on average, can hear sounds ranging in frequency from 20 Hz to 20,000
Hz. We associate frequency with the “pitch” of the note, like in music. The
loudness of a sound is measured in deciBels, a scale that compares the intensity
of a sound to the threshold of human hearing (I0 = 10-12 W/m2). A normal
conversation is around 60 dB. A rock concert is around 110 dB. The threshold of
pain is around 130 dB.
Prolonged and frequent exposure to loud sounds can cause temporary or
permanent hearing damage. Workplace safety regulations state that 85 dB is
safe for a duration of 8 hours. For every increase of 3 dB, the exposure time
should be reduced by half.
Loudness and Intensity
The loudness (L) and intensity (I) are related through the following equation:
With a bit of math, we can show that the difference in loudness of two sounds is:
From here, we can see a common rule that doubling the intensity is equivalent to
increasing the loudness by 3 dB.
Technological Applications
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Sonar uses echolocation to produce images and maps of the sea beds.
Ultrasounds use high frequencies (above human hearing) to produce
images of tissue in the body and is often used to follow the development of
a fetus in the womb. Sound waves are safe whereas X-rays are harmful to
tissue and especially to the fetus.
There are military weapons that use sound of high intensity (above the
threshold of pain) to disperse rioting crowds. Some high pitch frequencies
at high intensity can also induce nausea and vomiting besides the physical
pain of the sound.
Success Criteria
The students understand that sound waves are three-dimensional longitudinal
waves and can properly use the terminology to discuss waves.
The students can carry out the lab experiment measuring the speed of sound,
creating a hypothesis for the speed of sound based on the formula given.
The students can solve problems involve wave motion using the universal wave
equation and the speed of waves equations.