Resonance , Standing Waves, and the Doppler Effect

London’s Millenium Bridge Review Resonance The amplitude of any vibrating object can be greatly increased by applying small external forces at specific regular intervals of time. The time interval between applied forces must be equal to the period of the oscillations. London’s Millenium Bridge This effect is called mechanical resonance. In sound applications, a resonant frequency is a natural frequency of vibration determined by the physical parameters of the vibrating object. Sound Resonance!

Nodes and Antinodes Standing waves consist of a series of stationary nodes ( N ) and antinodes ( A ). A A N N N Nodes are regions which always appear to be standing still. They are regions with no displacement. They occur when the reflected wave destructively interferes with the incident wave. Antinodes are regions where the medium has the maximum displacement. They occur when the reflected wave constructively interferes with the incident wave.

Musical Instruments and Resonance! -musical instruments produce sound from air resonating through the tubes. - All instruments like this can be divided into two categories, open ended or closed ended. *An open ended instrument has both ends open to the air. *The keys on the trumpet allow the air to move through the"pipe" in different ways so that different notes can be played. *A closed ended instrument has one end closed off, and the other end open. *The frequencies of sounds made by these two types of instruments are different because of the different ways that air will move at a closed or open end of the column. Time for Question of the slide: What type of instrument is a trumpet, a clarinet , a pipe organ and a flute?

Identifying Fractions of Wavelengths Sound waves travel in longitudinal form, but will be drawn as transverse waves in order to explain harmonics in an easier way. One wavelength (λ). Three quarters of a wavelength (3/4 λ) One quarter of a wavelength (1/4 λ). One half of a wavelength (1/2 λ).

The sounds the instrument columns make depends on how much of a wavelength can fit into the column. Different wavelengths in the column produce different frequencies being produced. (AKA sound pitch) The frequencies that are produced by these waves are the natural frequencies and we call them resonant frequencies. In music these are referred to as harmonics. Pushing different keys or controlling how hard you blow into the instrument contributes to the differences in notes. Ex. High C or Low C The lowest note you can play is the minimum wavelength that can fit into the column. This note is called the Fundamental Note. As more waves fit into the column more harmonics are played. They are all multiples of the fundamental wavelength. What?????? Let’s look at the different notes open and closed column instruments can produce!

Remember air is doing the vibratiting here! Closed Ended Columns! Remember air is doing the vibratiting here! ● The air at the closed end of the column must be a node (not moving), since the air is not free to move there and must be able to be reflected back. ● There must also be an antinode where the opening is, since that is where there is maximum movement of the air. This is the smallest wave portion that we can fit into a column with a node at one end and an anitnode at the closed end. The length of the wave above is ¼ of a wavelength. (even though it might not look like it.) Draw a wavelength and see. This is called the Fundamental, or 1st Harmonic.

The Fundamential or First Harmonic in a Closed Column... The 3rd Harmonic in a Closed Column... There is no such thing as a 2nd harmonic for closed end columns. Why? All of the harmonics in closed end columns are going to be odd numbers!

Fifth Harmonic in a Closed Column... ● There is one full wavelength in there (4/4) plus an extra ¼ of a wavelength for a total of 5/4. The length of the column is… Do you notice a pattern forming in the formulas? ● Notice how all the formulas for the closed end columns are something over four. ● The number on top is always an odd number that is the same as the harmonic.

Open Ended Columns! ● The fundamental (first harmonic) for an open end column needs to be an antinode at both ends, since the air can move at both ends. This is a ½ wavelength even though it is a portion of the wave we don’t usually use to show ½ wavelength. Fundamental for an open column, showing reflection.

Open end columns can have any number harmonic they want, odd or even. 2nd Harmonic... Open end columns can have any number harmonic they want, odd or even. Trace it out and you’ll see that there is exactly one wavelength here. Open end column second harmonic, showing reflection!

The pattern is still continuing... ● The number on top can be any even or odd number, the number of the harmonic. ● The bottom number is always 2 for open ended columns. Can you guess what the wavelength will fit in the tube to produce the 3rd harmonic?

Examples: 1.

A tunning fork is struck and produces a frequency of 256 Hz A tunning fork is struck and produces a frequency of 256 Hz. Determine the wavelength of the sound wavelength produced if the speed of sound is 343 m/s. A transverse water wave has an amplitude of 48 mm and a wavelength of 86mm. What is the vertical displacement from the top of a crest to the bottom of a trough? What is the length of a trough?

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