## Physics-SchoolUK.com

### The UK site for KS3 and KS4 Physics

#### KS3 3.4.1 Waves - Sound

We start this section with an introduction common to all waves, then we zoom in to focus on sound waves
Perhaps the most important thing we learn is that all waves transfer energy from one place to another without any movement of matter.

### Waves - Introduction

Sound and light travel as waves.

There are 2 types of wave, "longitudinal" and "transverse". These words describe the way the waves travel.
Sound is a good example of a longitudinal wave and light is a good example of a transverse wave.

How Waves Travel

All waves travel by means of some vibration (an up and down or a back and forth motion that repeats).
If the "thing" vibrates up and down or transverse to (which means, at right angles to) the direction of travel of the wave then the wave is of the Transverse type.
If the "thing" vibrates back and forth or along (or, in line with) the direction of travel of the wave then the wave is of the Longitudinal type.

The following simple diagrams should make the distinction clear.

What do these two types of wave look like?

1. If the vibration is Transverse to the direction of the wave eg Up and Down or Side to Side, then the resulting wave will look like this:

Notice the repeating pattern of peaks and troughs (maximums and minimums); this is a characteristic of a Transverse wave.

A simple way to make a transverse wave is to drop a stone into some water; the downward movement of the stone sets up a ripple across the surface of the water.

Another simple way to demonstrate a transverse wave is to get a skipping rope or any long rope, keep one end still, then vibrate the other end up and down. You will see a transverse wave on the rope.

Notice - the "thing" that vibrates or which causes the disturbance does not travel along the wave. The dropped stone merely drops into the water, doesn't it; the hand moving up and down doesn't travel along with the resulting wave, does it?

Light travels as a Transverse wave. It is caused by vibrating electric and magnetic fields which both vibrate transverse to the direction of the wave, as shown below.

2. If the vibration is Longitudinal to the direction of the wave eg to and fro (forward and backward) along the direction of the wave, then the resulting wave...is harder to picture !

The best way to picture such a wave is to use a "slinky". A slinky is a long spring which when stretched out, looks a bit like this:

To demonstrate a Longitudinal type of wave using a slinky, keep one end fixed and vibrate the other end to and fro (forward and backward)

Very quickly you will see a pattern develop in the spring coils where some of the coils are closer together than normal and others are further apart than normal. The areas where the coils are closer together, we call Compressions; the areas where the coils are further apart, we call Rarefactions.

The repeating pattern of Compression - Rarefaction - Compression - Rarefaction... continues along the slinky spring; this repeating pattern is a characteristic of a Longitudinal wave.

Sound travels as a longitudinal wave.

What is it that all waves do ?

All waves (sound waves, light waves, water waves etc) have one thing in common.
They all transfer energy from one place to another without any transfer of matter.

So, a sound wave produced by a loudspeaker will transfer energy from the vibrating cone inside the loudspeaker to another place (eg to the ear of a person listening) without any transfer/movement of the vibrating loudspeaker cone to the person and without any movement of the vibrating air particles to the person.

#### Sound waves

Where can sound travel?

Sound waves have to travel through a medium. They can't travel through a vacuum (a place where there is no solid, liquid or gas, such as in the "space" between planets and stars.)

Sound waves can travel through the air (which is a gas), such as when a person speaks to another person in a room.

But sound waves can also travel through solid and liquid mediums. Examples of these include: sound travels through a wooden door when a person outside knocks on the door and you hear it inside; sound travels through water (you can hear sounds when you swim under water).

In fact, sound waves travel faster when the medium is denser; it travels faster in liquid compared to through a gas (eg the air); it travels even faster through a solid!

Visualising a sound wave

As we said above, Sound travelling through the air consists of a series of compressions (where air particles are squashed together) and rarefactions (where air particles are spaced further apart).
Unfortunately it's not easy to visualize such a sound wave.

To make it easier we could ask a person to speak into a microphone connected to an oscilloscope.
The microphone converts the sound wave, produced by the person speaking, into an electrical signal which can be viewed on the oscilloscope.

When we do so, this is what we see on the oscilloscope screen:

The compressions (areas of high pressure) are the peaks; the rarefactions (areas of lower than normal pressure) are the troughs.

Using this pidture of a sound wave we can easily describe the wave.

Describing a sound wave

We use the words : amplitude, frequency and wavelength to desribe a wave.

1. Amplitude

The Amplitude of the wave is the maximum displacement of the wave from its rest/undisturbed position. So, the amplitude of our wave is indicated by the following :

Notice the letter a, used to represent Amplitude.
The amplitude can equally be indicated on the negative side of the wave, as follows :

Since amplitude is a distance, it is measured in metres, m.

In our everyday world, we don't often refer to the "amplitude" of a sound wave; instead we refer to its volume and it can be measured with a sound meter which gives the volume in a unit called a decibel, dB.

The larger the amplitude of a sound wave, the larger its volume; its a louder sound.

The smaller the amplitude of a sound wave, the smaller its volume; its a quieter sound.

So amplitude and volume have a very similar meaning.

2. Frequency

The frequency of a wave is the number of complete cycles of a wave in one second..
To illustrate Frequency we need to add a few numbers to our x-axis as shown below :

So, we can see that there are 2 complete cycles of the wave occuring in 1.0s. Hence, for this wave the Frequency, f is 2.
We could say, the Frequency, f = 2 cycles per second
but the preffered unit is the hertz, Hz, so we say:
The Frequency, f = 2 Hz.

In our everyday world, we don't often refer to the "frequency" of a sound wave; instead we refer to its pitch.

The larger the frequency of a sound wave, the higher its pitch.

The smaller the frequency of a sound wave, the lower its pitch.

So frequency and pitch have a very similar meaning.

The wave above with a frequency of only 2 Hz is an extremely low frequency / pitch, so low that a human would not hear it as a sound wave.
The lowest frequency that humans can detect as sound is 20 Hz (that would be 20 complete wave cyles in one second).
The highest frequeny that humans can detect as sound is 20,000 Hz (that would be 20,000 complete wave cycles in one second, a very high frequency!

The range of frequencies that a person can hear is known as the audible range for humans.
Other animals have different audible ranges, eg dogs can hear frequencies much higher than our 20 KHz limit.

3. Wavelength

The third word that is used to help to describe a sound wave (or any wave, in fact), is its wavelength.

The wavelength of a wave is the distance travelled by one complete wave cycle. If we visualise a sound wave travelling from a persons mouth, the wavelength would be the distance travelled by one wave.

To show this on a graph we would need to change the x-axis from time to distance travelled, as shown below.

The following diagram shows how we measure the wavelength of a wave:

One full wave cycle is from the first green dot to the second, so the distance between them is the wavelength, and the symbol for it is the greek letter λ.
Another way to show wavelength is the distance from the peak of one wave to the peak of the next, or from the trough of one wave to the trough of the next. See the following diagram:

Since wavelength is a distance it is measured in metres, m just like amplitue.

Wavelength and frequency are inversely related, meaning that as one increses the other decreases. So....

A long wavelength is equivalent to a low frequency / pitch.

A short wavelength is equivalent to a high frequency / pitch.

For a human the lowest frequency that we can hear is equivalent to a long wavelength of about 17m.
For a human the highest frequency that we can hear is equivalent to a very short wavelength of about 17mm.

The speed of sound

Sound travels very fast!

For example, through the air it travels about 330 metres in one second. So that's a speed of 330 m/s.

For comparison Usain Bolt, one of the world's fastest humans, takes 31 s to run 300 m.

But the speed of sound through the air is "slow" compared to its speed through a liquid or a gas.

Through a liquid such as water, sound travels at about 1500 m/s. This is why fish and whales rely more on their sound sensing ability than on their eyesight.

Through a solid such as concrete, sound travels at about 3700 m/s. That is 3.7 km in one second. That is fast!

However, if we compare the speed of sound to the speed of light, we would have to conclude that sound is not so fast after all.
Light travels at 300,000,000 m/s. That is 300 million metres in one second! So a sound wave through the air is a million times slower than light.

Sound waves can be reflected, transmitted or absorbed by different materials

Reflection of sound

The best example of reflection of a sound wave is an echo.

This occurs when a sound wave travelling through the air hits a relatively hard object; in the case of an echo the hard object is usually a distant mountain at the end of a valley.

So reflection of sound occurs when a sound wave strikes a relatively hard or dense object. The harder the better for a good echo.

A good example of making use of an echo is when a ship sends out a sound wave to work out the depth of the water. The diagram below shows a sound wave reflecting off the sea bed; knowing the time taken for the reflection to occur and the speed of sound in water, allows the captain to calculate the depth of the water.

This technique is known as echo sounding.

Transmission of sound

The fact that sound can be transmitted, meaning to pass through, is obvious when we consider that a person speaking is heard many metres away. The sound is being transmitted through the air.

Sound can also be transmitted through a liquid such as water and through a solid such as concrete; we discussed this above.

The only thing that sound will not be transmitted through is a vacuum, also mentioned above. A good example of the use of this knowledge is modern double glazed windows; they consist of two layers of glass with a vacuum in between; this considerably reduces sound passing through the window.

Absorbtion of sound

Although sound can be transmitted through a solid, a liquid or a gas, it doesn't get transmitted perfectly. For example, when a person speaks we do hear them a few metres away, but if we walk further and further away we will notice that the amplitude (or volume) of the sound will decrease. The air is absorbing the sound wave more and more as the distance from the speaker increases or as the "thickness" of the air gap increases.

However, air is not really a good absorber of sound. The best absorbers of sound are soft materials.
An air gap filled with wool or polystyrene will absorb sound quite well; they also won't reflect the sound back to its source.

When a sound wave meets an absorber, the energy of the sound wave is transferred to the absorber; a good absorber will take all of the energy from the sound wave such that no sound will pass through or be transmitted through the absorber.
When energy is transferred from the sound wave to the absorber the absorber actually heats up! This, however, would be hard to detect.

Now it is time for you to have a go at a few questions:

#### Keywords

Now that we have reached the end of this section we can focus on the keywords highlighted in the KS3 specification. You have already met each one, but it is important to learn them.

• Vibration: An up and down or a back and forth motion that repeats.
• Longitudinal wave: Where the direction of vibration is the same as that of the wave.
• Volume: How loud or quiet a sound is, in decibels (dB).
• Pitch: How low or high a sound is. A low (high) pitch sound has a low (high) frequency.
• Amplitude: The maximum amount of vibration, measured from the middle position of the wave, in metres.
• Wavelength: Distance between two corresponding points on a wave, in metres.
• Frequency: The number of waves produced in one second, in hertz.
• Vacuum: A space with no particles of matter in it.
• Oscilloscope: Device able to view patterns of sound waves that have been turned into electrical signals.
• Absorption: When energy is transferred from sound to a material.
• Auditory range: The lowest and highest frequencies that a type of animal can hear.
• Echo: Reflection of sound waves from a surface back to the listener.