Experiment Report: Finding the Speed of Sound by Air Column Resonance

This report details an experiment to determine the speed of sound in air using air column resonance. The experiment involved two methods: using a tuning fork and an audio frequency generator. In the first method, a tuning fork was struck and held above a resonance tube in water, and the tube length was adjusted to achieve the loudest noise, recording three different lengths against their frequency. The average frequency and tube length were calculated to find the velocity of sound, which was slightly higher than the theoretical value due to reading errors. The second method used an audio frequency generator and a speaker to disturb the air and produce a wave, with procedures similar to the tuning fork method. The experiment aimed to measure sound wave speed and compare the data to the theoretical value, considering the influence of air temperature. The findings affirm the inverse relationship between wavelength and frequency in sound waves.

Air Column Resonance 1

Air Column Resonance 2
Air Column Reson
FINDING THE SPEED OF SOUND BY AIR COLUMN RESONANCE
By Name
Class (Course) Name
Professor (Tutor)
School (University) name
The City and State where it is located
The Date

Air Column Resonance 3
FINDING THE SPEED OF SOUND BY AIR COLUMN RESONANCE
By Name
Class (Course) Name
Professor (Tutor)
School (University) name
The City and State where it is located
The Date
Abstract

Air Column Resonance 4
A sound wave is a longitudinal wave where the wave oscillates along the propagation direction.
Sound resonance can be used to calculate the speed of sound in air. The objective of the
experiment was to determine the sound speed in the air using two different methods. The tuning
fork was held just above the resonance tube, which was placed in water. The mallet was used to
strike the tuning fork. The objective was to achieve the loudest noise by adjusting the tube
length. Three different lengths of the resonance tube were recorded against their frequency. The
average frequency and average tube length were then calculated. The velocity of sound was then
found to 345.71m/s. The value was slightly higher than the theoretical value. This was due to an
error in taking the reading of the tube. The second experiment involved the use of an audio
frequency generator. A speaker was held at the top the tube. An audio frequency generator
offered the energy for speaker, which disturbed the air thus producing a wave, moves away from
the speaker. The other procedure were more similar to that of the tuning fork.
Keyword: Sound, wave, velocity, speed, wavelength, resonance tube

Air Column Resonance 5
Introduction
Sound can be defined as a longitudinal wave where the wave oscillates along the
propagation direction. The relationship of sound can be modeled using the following parameter,
let’s say, the wave is traveling at a speed v, and has a frequency of f and wavelength λ,
v=fλ
This experiment employed a typical traveling wave (the resonance) to find the
wavelength and ultimately the velocity or speed of the sound wave (Jewett & Serway, 2015).
Assuming a traveling sound wave through a resonance tube, fig 1 below.
A tuning fork is normally held above the open end of this tube. Striking the tuning fork
using a rubber hammer will cause it to vibrate thus generating a sound wave (Loyd, 2013). The
sound wave then travels along the tube downwards and when reaches the water surface it is
reflected. These reflected sound waves interfere thus resulting in the formation of standing waves
(Equity, 2014). The reflected sound waves by the water surface shift their phase by 1800 making
them totally out of phase with the incidents sound waves (Loyd, 2014). It implies that at the
surface of the water, the amplitude of the standing wave is zero and this space point is known as

Air Column Resonance 6
a node. Provided the condition for resonance exists, the tube's open end will have standing
sound waves of maximum amplitude (anti-node) (Serway, Faughn & Vuille, 2016).
Sound speed is fixed provided temperature is kept constant. Besides, if the frequency is
fixed for every tuning fork the sound wave wavelength must also be fixed (Serway & Jewett,
2016). This means that conditions for resonance can only be satisfied when tube length is in such
a manner that Ln= 1
4 (2 n+1) λ where n=0,1,2,3,4,5,6 , … ….
Length Ln is the distance between the water surface and the tube open end. For n=0
The tube length L= 1
4 λ. For n=1 ,2 , 3 conditions, it is apparent that L2−L2= 1
2 λ ;
L3−L2= 1
2 λ ; This trend can be used to find the subsequent resonance L4 = 7
4 λ+ 1
2 λ= 9
4 λ and
this can be summarized as:
Ln+1 + Ln= 1
2 λ
∆ L=1
2 λ
. The relationship between two successive resonances can be utilized to establish the
wavelength ( λ ¿ is a standing sound wave. The objective of the experiment was to measure
sound wave speed in air and the tabulated data compared to the theoretical one.

Air Column Resonance 7
Speed or velocity of sound in the air mainly depends on air temperature and can be
connected using the relationship as indicated above. According to the theory, the speed of sound
in air depends upon the temperature of the air.
A system will oscillate at a maximum amplitude when it is at resonance. This takes place
at fundamental frequency nodes are generally points with zero amplitude. Antinodes are
basically points having maximum amplitude. As the sound wave travels through a resonance
tube, each end reflects it and this brings about interference. An open pipe, in the field of music
that has both ends open while a closed pipe that has one of the ends open and the other end
closed (Cassidy et al, 2014).
The amplitude is the wave deviation from the equilibrium position. There is sound
amplification when the sound waves motion in a pipe takes place at the open end. When the pipe

Air Column Resonance 8
has the standard, it occurs and there are very loud sounds showing resonance state of the tube.
The repeated waves that the source, for instance, the tuning fork continue constructively
combining with reflected waves thus forming resonance (Masters, 2015). It is simple because air
molecules in a tube with one end open can free oscillates back and forth. The molecule in a
closed tube has air molecules that limited to performing wide motions (White & White, 2014). It
means that a node is formed at a closed end while antinode can from in the open end provided
the length of the true value have the right length (Muncaster, 2013; Sen, 2016).
The figures below show how both minimum and maximum oscillation are formed at the
close and opens ends for a specific wavelength at varied lengths of the tube.
(Winn, 2015).
Convention and for simplicity reasons, transverse wave representation can be used to
display the minimum and maximum oscillation or motion at the closed and open ends (Tippens,
2017). Since sounds waves are longitude, which moves to and fro parallel to the length of the
tube as indicated above. The resonance tub length λ /4 for the open to produce an antinode
wavelength denote with the symbol λ is the distance between one bottom or peak to the next
bottom or peak. Frequency is the full wave number that is produced per second (Breithaupt,
2016).

Air Column Resonance 9
Sound can be described as a pressure moving through a given medium as mechanical
waves. Exerting a force on particles of any medium, the particles get compressed or passed
together thus only leaving behind an additional space, as well letting it expand. For domino
effects, the moving particles will exert force on the adjusted particle, the adjusted particles then
follow the trend and the process continues as a reaction chain. The pressure wave is formed by
compression repeating pattern as well as rarefaction. The wavelength thus becomes the distance
between the two compressions or between two rarefactions (Harrington & Cassidy, 2017).
Sound can travel in any medium. Sound does not travel in a vacuum. A vacuum is a
place with no matter and sound requires matter for its transmission. A number of factors affect
the velocity of sound. For instance, the distance between the molecules. When molecules are
very close to each other, the wave easily travels. Heavy molecules hinder the transmission of
waves. The temperature and the type of medium the sound travels in. it shows that velocity of
sound varies based on the material.
Objectives
 To find the speed or velocity of sound in air using a fork tune
 To find the velocity of sound in air using an audio frequency generator
Equipment
1. Tuning fork with a fundamental frequency of 440Hz
2. Rubber mallet
3. A large Graduated cylinder
4. Resonance tube apparatus about 2-3 cm in diameter and about 30 cm long

Air Column Resonance 10
5. A rule
6. And marking pen that can mark the glass
7. Audio frequency generator
8. Speaker
9. Connecting wires
Procedure
The first experiment involved the equipment being set up as the manual and graduated
beaker/cylinder filled with water to below the top. The glass tube was lowered until the top was
above the water surface.
Beginning with the water near the top of resonance tube, a tuning fork was struck with a
rubber mallet and placed on top of the glass tube. The level of water was slowly lowered until
the loudest sound was obtained. The level of water was marked at the highest sound heard. In
addition, the measurement of the distance between the top of the glass and the point the loudest
sound was heard was done. The resonance tube diameter was also measured and this help in the
calculation of the wavelength of the sound produced. The procedure was repeated for the other
two trials at different folk frequency.
Results
Data Trial 1 Trial
2
Trial
3
Average
Frequency of
tuning fork (Hz)
256 288 320 288
First Resonance 0.27 0.28 0.255 0.2683

Air Column Resonance 11
length (m)
Data analysis and Discussion
To calculate the average sound wave wavelength, it was important to note that the
generated sound waves in the resonance tube were mixed standing waves of the 1st harmonic
level. It implies L= λ
4 ∨λ=4 L in which L is the length of the resonant tube and λ is the
wavelength. For the calculation of wavelength, the following formula was employed:
λ=4 ( L+0.3 d ) where d is the resonance tube diameter and it takes care of the edge effects. The
tube diameter was 0.03m. after calculating the wavelength sound wave velocity was calculated
as
v=fλ
Because of resonance length l= λ/4
Hence
wavelength λ=4 ¿
v=288 ×1.109=319.448m/ s
The accepted sound velocity value is ¿ 341 ±1m/s
And with my value being 319.448m/s, it fell off within the theoretical value.
But taking the absolute sound wave speed at 342
The percentage difference 319.448−340
340 × 100=6.03 %

Air Column Resonance 12
The experimental value was lower than the theoretical value provided. This implies that
experimenter was almost accurate in his measurement and followed the experimental
instructions, except for some experimental errors, which accounted for the deviation (Silva,
2017). It makes sense to state that the results were quite accurate.
Through the exploitation of the resonance knowledge, and how resonance leads to a rise
in amplitude, we were successful at finding the average length of the resonance tube that the
frequency of sound should take to create the loudest sound. Natural frequencies can also be
found by increasing multiplication factor n. In the experiment, just a shorter air column length L
need to generate a resonating vibration in the air tube (Silva, 2017; Giordano, 2015). We
exploited the relationship between the resonance frequency, the resonance length, and
wavelength to find the wavelength. This allowed us to obtain the velocity of sound. The
uncertainty in the results involved approximating the resonant tube length from the tuning fork.
The experiment affirms the fact that wavelength and frequency are inversely proportional
especially when computing the velocity of sound waves. The attained results reveal that the
experimental room temperature was such close to that of room temperature. The humidity and
temperature just slightly deviated from the absolute value and hence never affected the
experimental results that much.
Questions
Question 1
The atmospheric conditions that might have affected the results included temperature.
Heat just like the sound is a form of kinetic energy. Molecules will have higher energy at a
higher temperature and this will cause them to vibrate faster. Due to the faster vibration of the