Standing, Open & Closed End Waves

Sound Waves : How do the Laws of Physic Explain Standing Waves and Harmonic FrequenciesMr. DelGiudiceHonors Physics Do Now Complete in next 5 min Define what wavelength and amplitude of a wave are and draw a picture of them.How do we define the frequency (of a wave)? What formula relates all of them?How does the speed of sound vary with temperature? Is the speed of a wave faster in a solid liquid or a gas? Why?What kind of wave is a sound wave? Longitudinal or Transverse. Your objective by the end of class: Be able to What are sound waves and how are they produced?Describe what is a standing sound wave and how they differ from each other. Describe what are harmonic frequencies and how do we visualize them through nodes and anti node diagramsCalculate simple fundamental harmonic frequencies forDemonstrate that physics laws govern harmonic frequencies for stringed instruments or open ended ended instruments . How do laws predict what frequencies an instrument can produce? Do all instruments give the same harmonic frequencies?3Frequencies Video

What is a Standing Wave?

What are their characteristics? A Standing wave is a wave produced by superposition of two periodic waves having identical frequencies and amplitudes which travel in opposite directions.

In a stringed instrument , the standing wave is produced by waves reflecting off a fixed end and interfering with the oncoming waves as the wave travels back through the medium..

In an opened end instrument , compressions and rarefactions cause the interference patterns..Closed at one end have a mixture of both of the above interference patterns. How are sound waves produced?Sounds are produced by vibrations Being a longitudinal standing wave , sound waves are characterized by regions of compressions ( condensation)and expansions( rarefactions) as they moves through a medium.

What are Sound standing wave characteristicsSounds . are produced by vibrationsbeing longitudinal waves it is characterized by regions of compressions ( condensation)and expansions( rarefactions) as it moves through a mediumare defined by frequency in Hz, wavelength in meters and velocity in(m/s).Pitch refers the frequency of sound in Hertz( Hz)

What is a Standing Sound wave again?A Sound wave Is a movement of a wave causing compressions and expansions of molecules longitudinally.Its source is that of simple harmonic motion It has a fundamental frequency, f ; a wavelength , and a velocity, vIt is represented by a standing wave and can produce harmonic frequencies predicted by physics laws.Can move through mediums at different speeds. speed of sound through air @ 0 C is 331 m/s

Has a fixed velocity, wavelength and speed.Can be measured for these characteristics Lets look at a standing waveto understand Harmonics:A look at nodes and anti nodes

Nodes and antinodes describe allowable frequencies

Nodes and anti nodes Make up standing waves

Nodes and Anti nodes and their drawingsNode : A point on the wave of minimal disturbance

Anti Node : A point on the wave where there is maximum disturbance

What are harmonic frequencies? Demo.. Alex, Alexie , Dawn Guitar Del : Clarinet , Guitar ,Harmonica

Listen to the harmonic sounds..

Guitars E note Harmonica ETuning fork E Piccolo or flute if presentWhich has a higher pitch or frequency?How are they related?Physics helps us to predict they are related?Lets look at what is harmonics?

Octaves are pairs of the Harmonic frequency Series

The 1st harmonic and the 2nd harmonic frequenciesare considered an octave apart.

n= 1 C 256 Hz = f1 n= 2 C 512 Hz = 2 f1 n= 3 C 768 HZ = 3 F1And so on Harmonic of a fundamental frequency

Harmonic frequencies what are they?What physics laws predict them??

Harmonic Frequencies

How are sound waves produced again? Listen to the instruments .DR D .. Alex , Alexie, Dawn others?

Answers??

How do Vibrating Strings or Vibrating Air Columns produce sounds of different frequencies?

How Physics help predict which instruments have high or low frequencies of sounds?

What are nodes and anti nodes again?

They represent maximum and minimum????????? Amplitudes!!

Nodes and anti NodesFor Open end or StringedClosed at one end Displacement anti nodes at both endsMust have at le have at least one length to have wave at all.Single node corresponds to f1.L = 1/2 or = 2Lfn = n v/2L v = speed of sound in airF n=2 = 2 v/2L= v/L = 2LAll integers allowable n= 1,2,3 ex flute

Displacement node always atclosed endAnti node at open endL = /4( that of open end)Odd harmonics n= 1,3,5,7 only allowedChang L or diameter get different soundEx Clarinet closed endLonger L lower ffSample Problem using Harmonic equation for Frequency.

Q1. What is the first harmonic frequency ( for n=1,) in a 2.5 meter long pipe that is open at both ends ? Assume speed of sound in air is 345 m/s?

f1 =

Q2. What is the fundamental frequency f1, a Guitar string when the speed of waves on the string is 115 m/s and the effective string length is 25 cm( 0.25m) ?

f1 =

Sample Problem using Harmonic equation for Frequency.

Q1. What are the first harmonic frequencies ( for n=1 ) in a 2.5 meter long pipe that is open at both ends ? Assume speed of sound in air is 345 m/s?

f1 =

Ans = 69 Hz

Q2. What is the fundamental frequency of a Guitar string when the speed of waves on the string is 115 m/s and the effective string length is 25 cm( 0.25m) ?

Ans= 230Hz

What would be the fundamental frequency and t he first overtone For a 26 cm long organ pipe at 343m/s velocity ( 20 Celsius) if it is

Opened at both ends n = ? , n= ?

Closed at one end n= ? , n= ? Challenge!!! Go for it!!!!!!Prize Time!!!!! By end of classString Lengths

30For the stringed or open ended harmonic frequencies

n = 1 1= 2 L F 1n = 2 2= L 2 F1 = F 2n = 3 2= 2L/3 3 F1 = F 3 n = 4 2= 1L/2 4 F1 = F 4

How many antinodes and nodes are there for the 3ndharmonic frequency? For the 5th?

Now can we measure Harmonic Frequencies? How?Open-end or stringed harmonic frequency formula f = v frequency times wavelength = velocitySince for an open ended pipe or stringed instrument : f = v since = 2L here L is length in mf = v for fundamental frequency 2L

For Closed at one end pipesfrequencies are odd!f = v frequency times wavelength = velocitySince for an closed ended pipe instrument since = 4L here L is length in m

f = v since = 4L here L is length in mf = (n) v for fundamental frequencies 4L n = 1,3,5,7, only odds

Check for understanding time..

Using the Frequency Harmonic motion equation for open ended or stringed instruments: f = n v/2L where n = 1 for fundamental and n= 2,3,4,5 for harmonic series Q1. What is the first harmonic frequency ( for n=1) for a wave in a 2.5 meter long pipe that is open at both ends ? Assume speed of sound in air is 345 m/s?Q2. What is the fundamental frequency of a Guitar string when the speed of waves on the string is 115 m/s and the effective string length is 62.5 cm( 0.625m) ? Look at hand out:

Harmonics for APMusic/Physics Theory!! Listening? String Measurement

Go to station 1 or 2 or 3 or 4

Work with your group to answer the work station questions given the problem shown

Be sure to write your answers on the sheet provided and show /draw any diagrams and show work for any calculations asked for.Be sure to discuss your answers among your group and elect one spokesperson for each group to report back out once the activity is completed and we are back at our desks.

Can You Measure Harmonic Frequencies of Instruments ?Step 1 : Use the flute in front of you. Using a meter stick and measure the actual length of the flute from the center of the ligature (mouth opening) to the longest end of the flute in cm. record the findings in cm and then change to meters to get the experimental length.Experimental length by measurement= ____________ cm == ________________m A flute is designed so that is plays a frequency (f ) when all the holes are covered the temperature is @20 Celsius ( v sound = 343 m/s)Step 2 : Consider the flute to be an opened at both ends pipe. Find the theoretical Length L of the flute assuming the fundamental frequency n = 1, assuming that the C frequency of 264 Hz is the fundamental frequency. Assume frequency = v / wavelength and wavelength = 2 x L So f = (n) v / 2L solve for LWhere f is frequency and v is velocity of sound and L is length to be calculated. n=1Work Station 1

Can you measure the fundamental frequency( n=1) of a flute with all holes closed?

Work Station 2. Sound and the Guitar ( stringed instrument )

The thickest string on the guitar is strung from the nut to the bridge . Some electric guitars measure 0.63 m from nut to bridge for the E or thickest string and has harmonic frequency, f 1, when pressing on the first fret of 329 Hz. For your guitar workstation , put your finger on the first fret and measure from the point you press on the string (middle of fret 1 )to the bridge in cm.

Change the measurement to meters ..

Assume frequency = v / wavelength and wavelength = 2 x L So f = (n) v / 2L solve for L assume n= 1Record this measurement, in ___ cm then change to __ metersAssuming you have a stringed instrument, f = v/2L Assume v = 343m/s in the room then calculate L in cm then m WORK STATION 3 Problem SOLVING!

Go to work station #3 and problem solve

Work individually and collectively as a group! Get the correct answers show all work!Work Station # 4 YOURE A NODE!!!! Or An ANTI_NODE???

Physics NODES and Anti NODES

Try to decipher the patterns and draw logical infer ances and answers!! HA HA

Please Answer Questions CorrectlyLook at hand out:

Harmonics for Theory Its the end of class: Are you able to.. Describes what are sound waves and how are they produced?Describe what is a standing sound wave and how they differ from each other. Describe what are harmonic fundamental frequencies and how do we visualize them through nodes and anti node diagrams.Calculate simple fundamental harmonic frequencies for harmonic vibrations through a tube or down a string?Demonstrate that physics laws govern harmonic frequencies for stringed instruments or open ended instruments . Can you calculate frequencies an instrument can produce? Do all instruments give the same harmonic frequencies?e 46

Q1 What type of waves represent sound waves?

How do stationary waves differ from one another? Q2 What formulas do we use in physics to determine harmonic open ended or stringed instruments?

Q3 What do you actually need to measure to determinethe harmonic frequency of a wave?Hand in your calculation for your check for understandingby en EXIT QUESTIONS .Ee47