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Ch 17: Superposition
All textbooksKnight Calc 5th EditionCh 17: SuperpositionProblem 17
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Chapter 17, Problem 17

The fundamental frequency of an open-open tube is 1500 Hz when the tube is filled with 0°C helium. What is its frequency when filled with 0°C air?

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Fundamental Frequency

The fundamental frequency is the lowest frequency at which a system oscillates. In the context of a tube, it is determined by the length of the tube and the speed of sound in the medium inside it. For an open-open tube, the fundamental frequency can be calculated using the formula f = v/2L, where v is the speed of sound in the medium and L is the length of the tube.
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Speed of Sound in Different Gases

The speed of sound varies in different gases due to differences in density and temperature. In general, sound travels faster in lighter gases like helium compared to heavier gases like air. At 0°C, the speed of sound in helium is approximately 972 m/s, while in air, it is about 331 m/s. This difference significantly affects the fundamental frequency of sound waves in a tube.
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Effect of Medium on Frequency

The frequency of sound produced in a tube is directly related to the medium filling the tube. When the medium changes, the speed of sound changes, which in turn alters the fundamental frequency. For an open-open tube, if the medium changes from helium to air, the frequency will decrease due to the lower speed of sound in air compared to helium, demonstrating the relationship between medium properties and sound frequency.
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Related Practice
Textbook Question
Two strings are adjusted to vibrate at exactly 200 Hz. Then the tension in one string is increased slightly. Afterward, three beats per second are heard when the strings vibrate at the same time. What is the new frequency of the string that was tightened?
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Textbook Question
A flute player hears four beats per second when she compares her note to a 523 Hz tuning fork (the note C). She can match the frequency of the tuning fork by pulling out the 'tuning joint' to lengthen her flute slightly. What was her initial frequency?
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Textbook Question
CALC You have two small, identical boxes that generate 440 Hz notes. While holding one, you drop the other from a 20-m-high balcony. How many beats will you hear before the falling box hits the ground? You can ignore air resistance.
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Textbook Question
A bass clarinet can be modeled as a 120-cm-long open-closed tube. A bass clarinet player starts playing in a 20° C room, but soon the air inside the clarinet warms to where the speed of sound is 352 m/s . Does the fundamental frequency increase or decrease? By how much?
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Textbook Question
A 170-cm-long open-closed tube has a standing sound wave at 250 Hz on a day when the speed of sound is 340 m/s . How many pressure antinodes are there, and how far is each from the open end of the tube?
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Textbook Question
BIO Deep-sea divers often breathe a mixture of helium and oxygen to avoid getting the 'bends' from breathing high-pressure nitrogen. The helium has the side effect of making the divers' voices sound odd. Although your vocal tract can be roughly described as an open-closed tube, the way you hold your mouth and position your lips greatly affects the standing-wave frequencies of the vocal tract. This is what allows different vowels to sound different. The 'ee' sound is made by shaping your vocal tract to have standing-wave frequencies at, normally, 270 Hz and 2300 Hz. What will these frequencies be for a helium-oxygen mixture in which the speed of sound at body temperature is 750 m/s ? The speed of sound in air at body temperature is 350 m/s .
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