For a given harmonic of a closed-end air column, relate the length of the air column to the harmonic frequency and the speed of sound in air (or the temperature of the air). Some problems involve comparisons to open-end air columns.
A 2.58-meter long, closed-end organ pipe can produce a collection of harmonic frequencies in the audible range from 20 Hz to 20000 Hz. Assuming a speed of sound in air of 347 m/s, determine the fifth highest frequency within this range.
5th Highest Frequency
Hz
Liz and Trey are working on the Speed of Sound Lab. They hold a vibrating sound source with a frequency of 496 Hz above a closed-end resonance tube and determine that it resonates when the air column is 17.2 cm in length and 51.6 cm in length. (Ignore end effects. And if you don't know what end effects are, then ignore that the problem says to ingore them.)
What is the next highest resonance length that Liz and Trey will find?
Next Highest Position
cm
What is the speed of sound (in m/s) in the air column?
Speed
m/s
A physics student is doing a resonance tube lab. She notices that resonance is observed for the first harmonic when the length of the closed-end air column is 23.1 cm. Determine the third harmonic frequency (in Hertz) for this air column. (Assume a speed of sound in air of 340 m/s.)
3rd Harmonic Frequency
The auditory canal of the outer ear is closed at one end by the ear drum and open to the surroundings at the other end. It serves as a closed-end resonator, amplifying certain sounds more than others. Assuming a speed of sound of 349 m/s, determine the fundamental frequency of a 2.63-cm long column of air.
Fundamental Frequency
Haley and Ariel are working on their Musical Instruments Project. They are creating a Palm Pipe Instrument using a collection of PVC tubes stoppered or sealed by a foam plug placed at varying heights within the tube. By tapping the open-end of the palm pipe against a surface (like your palm), the air column inside acts as a closed-end air column. Each palm pipe is 22.4-cm tall. Assuming a speed of sound of 344 m/s and a first harmonic wave pattern, determine …
(Ignore end effects … and if you don't know what an end effect is, then ignore the fact that you were told to ignore them).
… the length of the closed-end air column (in cm) to produce a 512 Hz sound wave.
Length
… the distance from the untapped end that the foam plug must be placed to seal the column.
Dist. from Untapped End
The fundamental frequency of an open-end organ pipe is 343 Hz. The third harmonic of a closed-end organ pipe has the same frequency. The speed of sound in air is 353 m/s.
Determine the length (in cm) of the open-end pipe.
Determine the length (in cm) of the closed-end pipe.
A closed-end air column resonates with a third harmonic frequency of 621 Hz.
Determine the fundamental frequency of an open-end air column that has the same length.
What is the frequency of the 7th harmonic of this open-end air column?
Frequency
A closed end organ pipe produces a fundamental frequency of 325 Hz. What would be the fundamental frequency of an open-end pipe that has the same length?