Week 2: Getting familiar with waves

1. In a recording room an acoustic wave was measured to have a frequency of 1 KHz. What would its wavelength in cm be?

Velocity (v) = Frequency (f) x Wavelength (λ) 

The velocity of sound in air is 340 m/s. Since we already know that the frequency of the wave is 1 KHz (or 1000 Hz) it is easy to work out the wavelength using the above equation. 

Wavelength (λ) = Velocity (v) / Frequency (f)

                     = 340 / 1000

                     = 0.34 m

Then we convert the value into cm. The wavelength is 34 cm.

2. If a violinist is tuning to concert pitch in the usual manner to a tuning fork what is the likely wavelength of the sound from the violinist if she is playing an A note along with sound from the pitch fork?

The frequency of an 'A' on the violin is 440 Hz and its wavelength is 0.77 m (λ = v/f). This is the same as the frequency and wavelength of a concert pitch A note tuning fork. Therefore the two sine waves will add together to form a wave with a frequency of 880 Hz and a wavelength of 0.39 m. (This is of course assuming that the violinist is actually in tune when she plays her A note.)

3. If an acoustic wave that is traveling along a work bench has a wavelength of 3.33 m what will its frequency be? 

Firstly we need to know what the material that the work bench is made from. For the purposes of this question lets presume it is made from wood. The velocity of sound in wood changes depending on the type of wood from about 3300 - 3600 m/s. The work bench is probably quite hard wood so about 3600 m/s should be okay. 

Frequency (f) = Velocity (v) / Wavelength (λ) 

                    = 3600 / 3.33

                    = 1081 Hz

Why do you suppose that is it easier for this type of wave to be travel through solid materials?

Sound travels faster through solids rather than in air because of the nature of gases and solids. Gases like air have particles with quite a lot of space around them, meaning that when the sound wave hits these particles and starts them moving they will take longer to reach the next particles. On the other hand, in solids the particles are packed really tightly together. Almost as soon as the sound wave hits one particle it will hit the next one because they are so close together. This makes the velocity of sound in solids much faster than in gases. 

4. Sketch a sine wave accurately of amplitude 10, frequency 20Hz. Your sketch should show two complete cycles of wave. What is the duration of one cycle? What is the relationship between the frequency and the duration of one cycle?

The relationship between the frequency and duration is Time (sec) = 1 / Frequency (Hz)

5. Research the topic “Standing Waves”. Write a detailed note explaining the term and give an example of this that occurs in real life. 

A standing wave (or stationary wave) is a wave that remains in the same position and does not move. Most sound waves that reach our ears are not standing waves. Normally waves travel outwards, slowly spreading out and losing strength. A standing wave is created when the wave is 'trapped' between two or more surfaces. Musical instruments work by using trapped sound waves to produce different pitches and tones (sounds with a particular pitch). To be a tone a group of sound waves has to be very regular and all exactly the same distance apart.

When the sound waves are produced or bounce back off the end of a container, if it is the perfect length for that certain wavelength then instead of interfering with each other and cancelling each other out, the waves will reinforce each other. If you could watch the reinforced waves it would look like they are standing still - which is why they are called standing waves.

All standing waves have nodes, where there is no wave motion, and antinodes, where the wave is largest. The nodes determine which wavelengths will fit into a certain container/musical instrument. 

6. What is meant by terms constructive and destructive interference?

Interference is caused when two waves meet while travelling along the same medium. 

Constructive interference is when the two waves have a displacement in the same direction. The displacement of the waves adds together to create a larger displacement.

Destructive interference is when the two waves have displacement in opposite directions. This causes them to cancel each other out or 'destroy' each other's displacement. 

7. What aspect of an acoustic wave determines its loudness?

The amplitude of an acoustic wave determines how loud is it. The volume of sound waves is measured in decibels (dB). 

8. Why are decibels used in the measurement of relative loudness of acoustics waves?

Decibels (dB) are used to measure the intensity or loudness of a sound. The decibel scale has to cover a vast range of sound intensities because the human ear is so incredibly sensitive. We can hear everything from whispers to jet engines. A jet engine is about 1,000,000,000,000 times louder than the quietest audible sound. 

On the decibel scale, 0 dB is the smallest audible sound. It is almost total silence but not quite. A sound 10 times more powerful than 0 dB is 10 dB, 100 times more powerful is 20 dB and 1,000 times more powerful is 30 dB. 

Some common sounds and their decibel ratings:
Almost total silence - 0 dB
A very quiet whisper - 15 dB
Normal conversation - 60 dB
A lawnmower - 90 dB
A car horn - 110 dB
A rock concert or a jet engine - 120 dB
A gunshot or firecracker - 140 dB

All these dB measurements were taken while standing near the sound. The further away you get from the source of the sound, the less powerful and intense it becomes.

Any sound above 85 dB can cause hearing loss. This loss is related both to the length you are exposed to the sound as well as its power or intensity. Eight hours of 90 dB sound can cause damage to your ears and any exposure to 140 dB sound causes immediate damage as well as pain. 

Younger people can hear a greater range of sounds than older people. This is because your hearing becomes damaged as you age and you are less able to pick up the higher frequencies. Some people can be hypersensitive to sound, which means that a normal level (such as conversation at 60 dB) will sound louder to them and may actually cause pain. 

9. How long does it take a short 1KHz pulse of sound to travel 20m verses a 10Hz pulse?

The frequency of a sound wave does not affect the time it takes to travel. Therefore the 1 KHz wave and the 10 Hz wave will take the same amount of time to travel 20 m.

We can work out the time using the equation Time (t) = Velocity (v) / Distance (d)

So the time taken = 340 / 20 = 17 seconds.

10. Does sound travel under water? If so what effect does the water have?

The speed of sound in water is 1500 m/s. It travels considerably faster through water than through air because in a liquid the particles are closer together than in a gas.


Summary of key learning points:

• The velocity of sound changes depending on what medium it is travelling through - the more solid the material the faster the velocity. 
• Interference refers to how the displacement of two waves interacts together, either by adding together or destroying each other.
• The frequency of a sound wave does not affect the time it takes to travel a certain distance. 
• Amplitude determines how loud a sound wave will be. The volume is measured in Decibels (dB). 

References:
Basic wave theory - http://www.passmyexams.co.uk/GCSE/physics/basic-waves-theory.html
BBC Bitesize (General properties of waves) -
http://www.bbc.co.uk/schools/gcsebitesize/science/aqa/waves/generalwavesrev3.shtml
Standing waves - http://cnx.org/content/m12413/latest/
Musical notes and their frequencies/wavelengths: http://liutaiomottola.com/formulae/freqtab.htm

Constructive and destructive interference: 

http://astro-canada.ca/_en/a2313.php and http://www.physicsclassroom.com/class/waves/u10l3c.cfm

Decibels: http://www.howstuffworks.com/question124.htm