Week 6 Lab 3

Lab 3

The lab this week was to create a wave and then mix different waves together to create a new wave. The waves were created using a fundamental and the harmonics of the fundamental.

Harmonic Number	1	2	3	4	5	6	7	8	9
Amplitude relative to Fundamental	1	0	1/3	0	1/5	0	1/7	0	1/9
Amplitude dB	0		-9.54		-13.9		-16.9		-19.1
Frequency	400		1200		2000		2800		3600

The initial wave (fundamental) was created by setting the sample rate to 8000Hz, 8 bit, mono, the frequency to 400Hz and the duration to 0.02 seconds. This created the following wave :

The fact that I set the frequency to 400Hz, meaning 400 waves per second, and the duration to 0.02 seconds results in 8 cycles of the wave being drawn as 400Hz/0.02s = 8.

Next I worked my way through the chart only creating the odd harmonics as waves i.e. 1 (fundamental), 3, 5, 7 and 9. I created all of these waves individually always leaving the sample rate the same but changing the frequency and the amplitude for every harmonic. I worked out the frequency by multiplication. The 3rd harmonic of the fundamental has a frequency 3 times greater, similarly, the 5th harmonic has a frequency 5 times greater and so on. 

To work out the respective amplitudes of the harmonics I used a simple equation. For the 3rd harmonic I did 1/3, I then took the log of the answer, I then multiplied it by 20 to give me the amplitude.

For the 3rd harmonic of the fundamental the data I input was amplitude -9.54 and frequency 1200Hz, the wave created was:

Similar to the fundamental wave the number of cycles was calculated by dividing the frequency, 1200Hz, by the time which was 0.02 seconds, resulting in 24 cycles of the wave. As previously explained the 3rd harmonic of the fundamental has a frequency 3 times greater therefore the number of cycles of the wave within the same time period is also 3 times higher, 8 compared to 24.

I performed the same operation on the other fundamentals and then I cut and mix pasted them all into one wave. As I did so I noticed that a square wave shape started to take form as I pasted each wave in one at a time. The resulting wave after I pasted all waves on top of the fundamental was:

Part two of this lab was very similar to part one, however, this time after creating the fundamental tone I was to create the 2nd harmonic upto the 5th harmonic and merge them with the fundamental pure tone. The table of data was worked out the same as it was above and was as follows:

Harmonic Number	1	2	3	4	5
Amplitude relative to Fundamental	1	1/2	1/3	1/4	1/5
Amplitude dB	0	-6.02	-9.54	-12.04	-13.9
Frequency	400	800	1200	1600	2000

The initial fundamental pure tone was created using the same parameters as I used above;8000Hz, 8 bit, mono, the frequency to 400Hz and the duration to 0.02 seconds. The wave created therefore was identical to the fundamental wave at the top of the page. However, because I am now adding in all the harmonic waves instead of just the odd numbers the resulting mixed wave is significantly different from that shown above.

The wave created is almost like mountains in a way. Also, as there are completely vertical inclines on the wave it makes it more like a digital wave as opposed to an analog wave. A digital wave only has 2 options, 1 or 0/ on or off, although it is not quite as simple a wave as that it is getting close to it.

Tutorial Week 2

Q1 In a recording room an acoustic wave was measured to have a frequency of 1KHz. What would its wavelength in cm be?

The wavelength is 0.333cm. I worked this out by doing the following calculation :

v = fλ

λ = v  = 333   = 0.333cm

       f     1000

Q2 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?

Q3 If an acoustic wave is traveling along a work bench has a wavelength of 3.33m what will its frequency be? Why do you suppose that is it easier for this type of wave to be travel through solid materials?

The frequency of the wave is 100Hz. I worked it out by doing the following:

v = fλ

f = v = 333  = 100Hz

      λ    3.33

Q4 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?

Here is shown two cycles of a sine wave with amplitude 10 and frequency 20Hz. The duration of one cycle is 1/20th of a second as the frequency tells us that 20 cycles will happen in 1 second therefore to find the period of one cycle you use the formula T = 1/f so T = 1/20.

Q5 Research the topic “Standing Waves”. Write a detailed note explaining the term and give an example of this that occurs in real life. (Where possible draw diagrams and describe what represent)

Standing(stationary) waves disturb but do not actually pass through the medium, it remains at a constant position. Stationary waves happen both in the air with sound waves and also in the ocean. If two waves collide because they are travelling towards each other the they cant go anywhere and become stationary.

Q6 What is meant by terms constructive and destructive interference?

Constructive interference is when two waves are happening at the same time but trough meets trough and peak meets peak. The two waves never touch but simply coexist.

Destructive interference is when the same two waves are not moving together and therefore trough meets peak and peak meets trough. The waves touch once a cycle and the resultant wave created by the two is a line.

Q7 What aspect of an acoustic wave determines its loudness?

The amplitude of an acoustic wave determines the loudness.

Q8 Why are decibels used in the measurement of relative loudness of acoustics waves?

Q9 How long does it take a short 1KHz pulse of sound to travel 20m verses a 10Hz pulse?

The time would be the same as the frequency of the sound does not effect the time taken to travel the same distance as speed remains constant at 333m/s.

Q10 Does sound travel under water? If so what effect does the water have?

Yes sound travels under water however it has a slower speed than in air so will take longer.

 

Digital Signal Processing Lecture

The Fundamental is the accumulation of all vibrations that merge together to create what is also known as the Basic tone. Other Vibrations however create a series of harmonic tones. The harmonic is a multiple of the fundamental tone(frequency) i.e. 2 x Fundamental, 3 x Fundamental.

The Amplitude of a sound wave is basically the height of half a wave, i.e. measured from the origin to the peak or trough. The higher/lower(or bigger/smaller) this is determines the level of the sound. For example, a wave with a high amplitude will strike the ear drum harder and therefore the sound is louder.
These measurements are hard to make and therefore sound is actually more often expressed in terms of Sound Level, measured in decibels.

All living creatures have and upper and a lower threshold of hearing which is the quietest or loudest a sound can be but also the frequency a sound can be to hear it. A humans threshold is different from other creature and therefore can hear different things.


Sound intensity = 10log10(Isound/IStandard) DB

The Inverse Square Law implies that the further you are from the source the quiter the sound is. Therefore a sound wave loses intensity over distance.
An echo however is the percieved copying of a sound due to reflection of the sound waves off of objects i.e. a tunnel. Time difference= (d1 + d2)/v
r(t) = s(t-d0/v)+alpha s(t-time dif)

Room reverb is similar to an echo with the exeption that it involves multiple reflections of the sound wave and the can all reflect back to the same point.

Sound Lecture

Transverse Wave - Ripple on the surface of the water and the ripples move from the disturbance in an outwards circular motion.

Longitudinal Wave - Vibrations move in parallel to the direction of the motion and also originate from the point of disturbance. Energy is passed between molecules leaving the first molecule in the same position i.e. newtons cradle.

Compression is a increase in the waves density.

Rarefraction is a decrease in the waves density.






Wavelength is calculated by the distance between two crests or troughs for a transverse waves and between two peak compressions for longitudinal waves.

The amplitude of a wave is its height from the origin to the peak of the wave i.e. half the height of a full wave.

Speed of sound - Metal   5000m/s
                         - Water  1500m/s
                         - Air   333m/s (350m/s??)

Frequency is defined as the number of waves to pass a point in 1 second and is measured in Hertz(Hz)

Velocity is defined as the speed at which the wave travels measured in metres per second(m/s)

Velocity = frequency x wavelength

Standing waves disturb but do not pass through the medium. violin strings vibrate with a node(minimum) at each end and an anti-node(maximum) in the middle. Note that nodes also occur in cavities such as a flute or a room. the nodes being in the walls and the anti-nodes being the middle of the room.