17.5 Sound Interference and Resonance: Standing Waves in Air Columns

We have emphasized sound applications in our discussions of resonance and standing waves, but these ideas apply to any system that has wave characteristics. Vibrating strings, for example, are actually resonating and have fundamentals and overtones similar to those for air columns. More subtle are the resonances in atoms due to the wave character of their electrons. Their orbitals can be viewed as…

We have emphasized sound applications in our discussions of resonance and standing waves, but these ideas apply to any system that has wave characteristics. Vibrating strings, for example, are actually resonating and have fundamentals and overtones similar to those for air columns. More subtle are the resonances in atoms due to the wave character of their electrons. Their orbitals can be viewed as…

A common misconception is that two wave pulses traveling in opposite directions will reflect off each other. Outline a procedure that you would use to convince someone that the two wave pulses do not reflect off each other, but instead travel through each other. You may use sketches to represent your understanding. Be sure to provide evidence to not only refute the original claim, but to support y…

A student sends a transverse wave pulse of amplitude A along a rope attached at one end. As the pulse returns to the student, a second pulse of amplitude 3A is sent along the opposite side of the rope. What is the resulting amplitude when the two pulses interact?

1. 4A
2. A
3. 2A, on the side of the original wave pulse
4. 2A, on the side of the second wave pulse

A student is shaking a flexible string attached to a wooden board in a rhythmic manner. Which of the following choices will decrease the wavelength within the rope?

1. The student could shake her hand back and forth with greater frequency.
2. The student could shake her hand back in forth with a greater amplitude.
3. The student could increase the tension within the rope by stepping backwards from the bo…

A tube is open at one end. If the fundamental frequency f is created by a wavelength λ, then which of the following describes the frequency and wavelength associated with the tube’s fourth overtone?

When a student blows across a glass half-full of water, a resonant frequency is created within the air column remaining in the glass. Which of the following can the student do to increase this resonant frequency?

1. Add more water to the glass.
2. Replace the water with a more dense fluid.
3. Increase the temperature of the room.

1. I only
2. I and III
3. II and III
4. all of the above

A student decides to test the speed of sound through wood using a wooden ruler. The student rests the ruler on a desk with half of its length protruding off the desk edge. The student then holds one end in place and strikes the protruding end with his other hand, creating a musical sound, and counts the number of vibrations of the ruler. Explain why the student would not be able to measure the sp…

A musician stands outside in a field and plucks a string on an acoustic guitar. Standing waves will most likely occur in which of the following media? Select two answers.

1. The guitar string
2. The air inside the guitar
3. The air surrounding the guitar
4. The ground beneath the musician

A student connects one end of a string with negligible mass to an oscillator. The other end of the string is passed over a pulley and attached to a suspended weight, as shown above. The student finds that a standing wave with one antinode is formed on the string when the frequency of the oscillator is f₀. The student then moves the oscillator to shorten the horizontal segment of string to half its…

A “showy” custom-built car has two brass horns that are supposed to produce the same frequency but actually emit 263.8 and 264.5 Hz. What beat frequency is produced?

What beat frequencies result if a piano hammer hits three strings that emit frequencies of 127.8, 128.1, and 128.3 Hz?

(a) What is the fundamental frequency of a 0.672-m-long tube, open at both ends, on a day when the speed of sound is 344 m/s? (b) What is the frequency of its second harmonic?

What are the first three overtones of a bassoon that has a fundamental frequency of 90.0 Hz? It is open at both ends. (The overtones of a real bassoon are more complex than this example, because its double reed makes it act more like a tube closed at one end.)

What length should an oboe have to produce a fundamental frequency of 110 Hz on a day when the speed of sound is 343 m/s? It is open at both ends.

(a) Find the length of an organ pipe closed at one end that produces a fundamental frequency of 256 Hz when air temperature is $18.0ºC$. (b) What is its fundamental frequency at $25.0ºC$?

The ear canal resonates like a tube closed at one end. (See the reference.) If ear canals range in length from 1.80 to 2.60 cm in an average population, what is the range of fundamental resonant frequencies? Take air temperature to be $37.0ºC$, which is the same as body temperature. How does this result correlate with the intensity versus frequency graph (the reference of the human ear?

A crude approximation of voice production is to consider the breathing passages and mouth to be a resonating tube closed at one end. (See the figure.) (a) What is the fundamental frequency if the tube is 0.240-m long, by taking air temperature to be $37.0ºC$? (b) What would this frequency become if the person replaced the air with helium? Assume the same temperature dependence for helium as for air.

What frequencies will a 1.80-m-long tube produce in the audible range at $20.0ºC$ if: (a) The tube is closed at one end? (b) It is open at both ends?