MPM School-Based Assessment Physics Project 2014/2015

Topic : To determine the velocity of sound in air at ordinary temperature by using resonance in an open ended cylindrical tube

School : S.M.K Kepong

Group Leader : Tan Sook Yin

Group Member : Lam Hoi Wing

Class : U6S2

Teacher : Puan Noratiqah

Abstract•v=fλ Where v=velocity of sound propagation , f= frequency , λ=wavelength

• The velocity of sound wave in air at room temperature (25°C ) is predicted to be 346.13 ms-1 even when the frequency is changed.

• The idea that sound moves in waves goes back (at least) to about 240 B.C. The Greek philosopher Chrysippus (c. 240 B.C.), the Roman architect and engineer Vitruvius (c. 25 B.C.), and the Roman philosopher Boethius (A.D. 480-524) each theorized that sound movement might take a wave form.

• Standing waves (also known as stationary waves) are set up as a result of the superposition of two waves with the same amplitude and frequency, traveling at the same speed, but in opposite directions.

• Any waves traveling along the medium will reflect back when they reach the end. This effect is most noticeable in musical instruments where, at various multiples of a vibrating string or air column's natural frequency, a standing wave is created, allowing harmonics to be identified.

• In this experiment we will create longitudinal standing waves in a tube containing air in order to measure the velocity of sound wave.

Introduction

Literature ReviewLeonardo di ser Piero da Vinci • Italian polymath, painter, sculptor,

architect, musician, mathematician, engineer, inventor, anatomist, geologist, cartographer, botanist, and writer.

• first person to discover that sound traveled in waves back in 1500.

Galileo Galilei • Italian physicist, mathematician, engineer,

astronomer, and philosopher who played a major role in the scientific revolution during the Renaissance.

• He demonstrated that the frequency of sound waves determined the pitch.

Marin Mersenne• French theologian,

philosopher, mathematician and music theorist, often referred to as the "father of acoustics“

• Marin Mersenne devised three laws to calculate the frequency of the fundamental tone produced by a string.

Robert Boyle• Irish natural philosopher,

chemist, physicist, and inventor.

• Boyle demonstrated that the sound of a bell in the receiver faded as the air was removed, proving that air was necessary for the transmission of sound.

Sir Isaac Newton• English physicist and

mathematician.• The first known theoretical

treatise on sound was provided by Sir Isaac Newton in his Principia, which predicted a value for the speed of sound in air that differs by about 16 percent from the currently accepted value.

METHODOLOGY

• The velocity of the sound wave is given by v = fλ , -----(1)

where f is frequency and λ is wavelength.• Length of air column where standing wave occur is

given by L= nλ/4 , where n is harmonic number (n= 1, 3, 5, …)• From L= nλ/ 4 , λ = 4L/ n -----(2)• Substituting (2) into (1) ,• From (1) : v = fλ v = f (4L / n) where f is frequency of sound wave, L is the length of air column where standing wave occur, and n is harmonic number ( n = 1, 3, 5, …).

RESULT

Frequency,

f / Hz

Length of air column at harmonic number

n=1, L / m

Wavelength,  λ / m

[λ = 4L /n]

 

Velocity,

v/ ms-1

 

[v = f(4L / n)]L1 L2 L3

Laverage

 

349.2 0.28 0.26 0.21 0.25 1.00 349.20

392.0 0.23 0.27 0.19 0.23 0.92 360.64

440.0 0.19 0.22 0.19 0.20 0.80 352.00

493.9 0.19 0.16 0.19 0.18 0.72 355.61

523.2 0.15 0.17 0.18 0.17 0.68

 

355.78

Discussion• The velocity of sound when frequency is 349.2 Hz, 392.0 Hz, 440.0 Hz, 493.9 Hz and 523.2

Hz are 349.20 ms-1 , 360.64 ms-1 , 352.00 ms-1 , 355.61 ms-1 and 355.78 ms-1 respectively. • The average experimental value for velocity of sound at room temperature (25°C) is 354.65

ms-1 , which is greater than the expected or actual velocity of sound, 346.13 ms-1 by 2.46 % due to several reason.

Reason Why The Experimental Value Of The Velocity Of Sound Is

greater Than The Actual Value

Surrounding air humidity

Assumption that the air molecules

cannot vibrate at the closed end (water surface)

which in fact not all waves reflect off the

water barrier

Surrounding temperature

Qualitative observation

Position of the tuning

forkParallax error

Conclusion• Based on the result we obtained in this

experiment, the velocity of sound wave at room temperature 25.0°C is 354.65 ms-1, which slightly greater from the expected velocity, 346.13 ms-1 by 2.46 %.

Reference

1. https://www.youtube.com/watch?v=CM5IFM0N1bE2. http://cgscomwww.catlin.edu/sauerb/PhysB/PhysB_Labs/

PhysB_Lab_04_Speed_of_Sound_Resonance.htm3. http://physics.info/waves-standing/4. http://en.wikipedia.org/wiki/Standing_wave5. http://en.wikipedia.org/wiki/Leonardo_da_Vinci6. http://thinkjarcollective.com/articles/creative-thinking-leonardo-

da-vinci/7. http://en.wikipedia.org/wiki/Galileo_Galilei8. http://www.electricalfacts.com/Neca/Science/sound/history.shtml9. http://en.wikipedia.org/wiki/Isaac_Newton10.http://en.wikipedia.org/wiki/Marin_Mersenne11.http://en.wikipedia.org/wiki/Robert_Boyle12.http://www.pci.tu-bs.de/aggericke/Personen/

Boyle_Biography.html 13.http://hyperphysics.phy-astr.gsu.edu/hbase/class/phscilab/

restube2.html