Review – Standing Waves

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Presentation transcript:

Review – Standing Waves What are the things that can affect the velocity of a string? The force of tension and thickness of string (linear density) What are the two parts of a standing wave? Which part produces the most sound? Nodes – little to no movement Anti-node – lots of movement Anti-node produce the most sound Term for the ‘voice’ of the instrument? Timbre

Difference Between Notes and Noise Sound (musical notes) will have some sort of repeating pattern

Standing Waves w/ Musical Instruments Tuning Forks – Produce one frequency (pure tone) Musical instruments sound different from tuning forks – due to their timbre (tone quality or tone color) Difference in timbre – due to the instruments harmonics When a note is played, the primary sound = Fundamental frequency Within each fundamental frequency are other frequencies – The harmonics

Standing Waves - Strings Different frequencies are produced by different harmonics Fundamental First Harmonic (f1) Number of Loops = 1 Second Harmonic (f2) Number of Loops = 2 f2 =2(f1) Third Harmonic (f3) Number of Loops = 3 f3 =3(f1) Fourth Harmonic (f4) Number of Loops = 4 f4 =4(f1)

Standing Waves - Strings With the fundamental AND harmonics sounding at the same time, the wave looks like…. cello

Standing Waves - Strings Frequencies for standing waves: n = number of the harmonic L = Length of the vibrating string v = velocity of a string *Different notes are achieved by changing the length of the vibrating string.

Example 11 A violin string is under a force of tension of 87.0 N. The vibrating portion of the string is 32.0 cm long and has a mass of 0.35 g. The string begins vibrating, creating a fundamental frequency. What is the velocity if this string under such conditions? What is the fundamental frequency produced? What are the values of the second and third harmonics for this fundamental?

Example 12 A string of length 0.26 m is fixed at both ends. The string is plucked and a standing wave is set up that is noticeably vibrating at its second harmonic. The traveling waves that make up the standing wave have a speed of 155 m/s. What is the frequency of vibration?

Standing Waves – Woodwinds and Brass These instruments create standing waves using vibrating columns of air Two Categories: Instruments (Pipes) Open at Both Ends All brass instruments, flute, organ Instruments (Pipes) Open at One End Most reed and double-reed instruments: Clarinet, Oboe, Saxophone, Bassoon, etc..

Standing Waves – Pipes Open at Both Ends *Standing waves have nodes and anti-nodes. The part that can create sounds (vibrations) is the anti-node *Need an anti-node at both ends Fundamental 1st Harmonic 2nd Harmonic 3rd Harmonic 4th Harmonic

Standing Waves – Pipes Open at Both Ends Frequencies for standing waves: n = number of the harmonic L = Length of the vibrating column of air **v = velocity of sound in air (343 m/s) *Different notes are achieved by changing the length of the vibrating column of air