1.Introduction

Project title: Investigation of the effect of frequency on the resonance effect of sound in an open pipe


as the title suggests, we are finding out how the frequency of a sound wave affects the resonance. we wanted to research into this topic because waves are used in many daily things such as microwaves. The effects of waves, such as resonance, are applied in things such as car bumpers


At specific frequencies and distances, the sound might seem larger, this is called resonance, it happens when two waves of equal frequencies at certain frequencies collide , producing a larger force. this is not only observed in sound
but also things such as suspension bridges, walls, floors, car shock absorbers , in these cases, we would not want them to resonate


we know that at certain frequencies the sound produced will be louder due to resonance. By measuring the loudness at certain frequencies, we should notice an increase in loudness at the frequencies that resonates


but if we test every frequency that would take too long, even if we only test audible frequencies, that would be 20 000 frequencies! we researched into how we can predict the frequencies that produces resonance with a specific length between the two sound sources. we found a formula that does this.
frequency=velocity/ (2)(length)

with this formula we can find out which frequencies to expect resonance, hence we create a hypothesis that resonance will form at those frequencies at a distance of 1m



1.1 Research Questions 



1) What are sound waves?


2) If sound waves are pressure waves, can they be used to levitate objects?


3) What are the applications of acoustic levitation?


4) how to get standing waves?


5) what are pressure nodes?


6)what is the formula for the amount of waves in a closed pipe


1) Sound is all around us everyday but we probably don’t think of sound as a physical presence. We hear sounds, we don't touch them. the only exceptions may be in loud nightclubs, cars with window-rattling speakers and ultrasound machines that make you feel like your innards are being moved. But even then, you most likely don’t think of what you feel as sound itself, but as the vibrations that sound creates in other objects. The idea that something so simple can lift objects can seem unbelievable, but it's a real phenomenon. Acoustic levitation takes advantage of the properties of sound to allow solids, liquids and even heavy gases to float. (How stuff works, 2007)


2) In the past, scientists have used everything from laser beams to superconducting magnetic fields to levitate objects.The principle behind the acoustic levitation is simple: Sound waves, which are waves of high and low pressure that travel through a medium such as air, produce force."We've all experienced the force of sound — if you go to a rock concert, not only do you hear it, but you can sometimes feel your innards being moved," Drinkwater told Live Science. "It's a question of harnessing that force."By tightly orchestrating the release of these sound waves, it should be possible to create a region with low pressure that effectively counteracts gravity, trapping an object in midair. If the object tries to move left, right, up or down, higher-pressure zones around the object nudge it back into its low-pressure, quiet zone.But figuring out the exact pattern of sound waves to create this tractor force is difficult, scientists say; the mathematical equations governing its behavior can't be solved with a pen and paper.(Live Science, 2015)


3) What are the applications of standing waves and harmonics?


“Microwave ovens. The frequency of the microwaves in an oven, 2.45 GHz, was chosen to give moderate absorption by typical food. (Too little absorption wastes energy, too much just crisps the surface of things.) But the corresponding wavelength, 12.5 cm, is a bit of a nuisance, because if you pump microwaves of that wavelength into a metal box, you get standing waves of that size, which is pretty big compared to food. That means you need a turntable to make sure that the food doesn't linger in a hot spot and cook unevenly.” (Quora, 2014)


“In the context of music, how high or low a note is depends on the frequency of the sound wave.


In string instruments, a plucked or bowed string makes the note is does because only certain frequencies of stationary (or "standing") waves are able to form on that string under those conditions (e.g., a finger holding down the string at a certain position). Any vibrations that aren't at the right frequencies to make standing waves quickly cancel themselves out, and so it's the standing wave frequencies that we actually hear.


Similarly, for woodwind instruments, we get the notes we get because of what standing waves are able to form within the tube of air inside the instrument.


Strings and woodwinds sound different from one another because they allow different combinations of overtones (higher-frequency standing waves) to form.” (Quora, 2014)


4) how do you get standing waves?


“A standing wave pattern is a vibrational pattern created within a medium when the vibrational frequency of the source causes reflected waves from one end of the medium to interfere with incident waves from the source. This interference occurs in such a manner that specific points along the medium appear to be standing still. Because the observed wave pattern is characterized by points that appear to be standing still, the pattern is often called a standing wave pattern. Such patterns are only created within the medium at specific frequencies of vibration. These frequencies are known as harmonic frequencies, or merely harmonics. At any frequency other than a harmonic frequency, the interference of reflected and incident waves leads to a resulting disturbance of the medium that is irregular and non-repeating.”(The physics classroom, 1996)
5) what are pressure nodes?


One characteristic of every standing wave pattern is that there are points along the medium that appear to be standing still. These points, sometimes described as points of no displacement, are referred to as nodes. There are other points along the medium that undergo vibrations between a large positive and large negative displacement. These are the points that undergo the maximum displacement during each vibrational cycle of the standing wave. In a sense, these points are the opposite of nodes, and so they are called antinodes. A standing wave pattern always consists of an alternating pattern of nodes and antinodes. The animation shown below depicts a rope vibrating with a standing wave pattern. The nodes and antinodes are labeled on the diagram. When a standing wave pattern is established in a medium, the nodes and the antinodes are always located at the same position along the medium; they are standing still. It is this characteristic that has earned the pattern the name standing wave.”(The physics classroom, 2000)


6) what is the formula for the frequency of sound resonance  in a open pipe


f=v/2L


‘f’ is frequency where ‘v’ is the velocity of sound, ‘L’ being the length of the pipe and the number before the ‘L’ being the number of wavelengths produced  


In our experiment, we know the velocity of sound, the length of our pipe , by inputting the amount of wavelengths , we can find out roughly what frequencies to expect for resonance to occur 


(a) Aim / question being addressed 


To find out which are the f
requencies that resonance occurs at distance of sound source being 1m


(b) Independent variable


The frequency being imputed into the speakers

165Hz

330Hz

495Hz

660Hz

825Hz

990Hz



(c) Dependent variable


Decibel reading when independent variable frequencies are being imputed



(d) Controlled variables/constant variables


(a) Speakers used
(b) The decibel meter used a
(c) Location where experiment is carried out(no wind)
(d) Distance kept between the two speakers
(e) The placement of the tube and speakers(not to be moved throughout experiment)
(f) The distance of the decibel meter from the tube



     1.2 Hypothesis

The sound will be louder at the frequencies 165 hz, 330 hz, 495 hz, 660 hz, 825 hz and 990 hz, and the decibel meters reading will increase significantly

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