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1. How many complete wavelengths are present? Can you vary the frequency to find a lower number of wavelengths that still produces a resonance? How many wavelengths? What is the frequency? Can you vary the frequency to find a fraction of a wavelength that produces a resonance? What is the fractional part of the wavelength? What is the frequency? 2. Set the wave speed to 48 m/s. What shorter length gives a resonance? Can you find a second even shorter length? What is the length? What fraction of a wavelength is present? 3. Suppose you wanted to select a string for a piano that would have a fundamental frequency of 64 Hz (2 octaves below middle C). The speed of the wave in this string is 95 m/s. Calculate the shortest length for this string. Confirm by simulation. 4. Calculate the 2nd and 3rd harmonic frequencies for the string above. 5. Uncheck "closed/open tube" so that you now have a tube with the right end open. (Keep the wave speed at 40 m/s.) For fundamental frequency of 20 Hz, calculate the length of the tube. Calculate the frequencies of the next two overtones and corresponding wavelengths for this tube. Confirm resonances in simulation.

1. How many complete wavelengths are present? Can you vary the frequency to find a lower number of wavelengths that still produces a resonance? How many wavelengths? What is the frequency? Can you vary the frequency to find a fraction of a wavelength that produces a resonance? What is the fractional part of the wavelength? What is the frequency? 2. Set the wave speed to 48 m/s. What shorter length gives a resonance? Can you find a second even shorter length? What is the length? What fraction of a wavelength is present? 3. Suppose you wanted to select a string for a piano that would have a fundamental frequency of 64 Hz (2 octaves below middle C). The speed of the wave in this string is 95 m/s. Calculate the shortest length for this string. Confirm by simulation. 4. Calculate the 2nd and 3rd harmonic frequencies for the string above. 5. Uncheck "closed/open tube" so that you now have a tube with the right end open. (Keep the wave speed at 40 m/s.) For fundamental frequency of 20 Hz, calculate the length of the tube. Calculate the frequencies of the next two overtones and corresponding wavelengths for this tube. Confirm resonances in simulation.

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Standing Waves I. User Interface and Simulation Features This simulation provides a stylized graphic of a wave on a string or a tube with one open end. The point of this experiment is to find combinations of length, wave speed and frequency that make naturally resonant systems (standing waves). You may choose the speed of the wave, the frequency of the wave, and the length of the tube or string. The timer and the oscillations of the string or the air in the pipe are synchronized. Both operate much slower than real time. At long wavelengths and low frequencies, the simulation speed may be increased with the slider bar in order to gain results more quickly. II. Questions In each case when you start a simulation for the following questions, reset the values using the icon in the control panel at the left side of the screen. Each question assumes that you have done this. Then set only the values indicated in the question. 1. How many complete wavelengths are present? Can you vary the frequency to find a lower number of wavelengths that still produces a resonance? How many wavelengths? What is the frequency? Can you vary the frequency to find a fraction of a wavelength that produces a resonance? What is the fractional part of the wavelength? What is the frequency? 2. Set the wave speed to 48 m/s. What shorter length gives a resonance? Can you find a second even shorter length? What is the length? What fraction of a wavelength is present? 3. Suppose you wanted to select a string for a piano that would have a fundamental frequency of 64 Hz (2 octaves below middle C). The speed of the wave in this string is 95 m/s. Calculate the shortest length for this string. Confirm by simulation. 4. Calculate the 2nd and 3ªd harmonic frequencies for the string above. 5. Uncheck “closed/open tube" so that you now have a tube with the right end open. (Keep the wave speed at 40 m/s.) For fundamental frequency of 20 Hz, calculate the length of the tube. Calculate the frequencies of the next two overtones and corresponding wavelengths for this tube. Confirm resonances in simulation.
Transcribed Image Text:Standing Waves I. User Interface and Simulation Features This simulation provides a stylized graphic of a wave on a string or a tube with one open end. The point of this experiment is to find combinations of length, wave speed and frequency that make naturally resonant systems (standing waves). You may choose the speed of the wave, the frequency of the wave, and the length of the tube or string. The timer and the oscillations of the string or the air in the pipe are synchronized. Both operate much slower than real time. At long wavelengths and low frequencies, the simulation speed may be increased with the slider bar in order to gain results more quickly. II. Questions In each case when you start a simulation for the following questions, reset the values using the icon in the control panel at the left side of the screen. Each question assumes that you have done this. Then set only the values indicated in the question. 1. How many complete wavelengths are present? Can you vary the frequency to find a lower number of wavelengths that still produces a resonance? How many wavelengths? What is the frequency? Can you vary the frequency to find a fraction of a wavelength that produces a resonance? What is the fractional part of the wavelength? What is the frequency? 2. Set the wave speed to 48 m/s. What shorter length gives a resonance? Can you find a second even shorter length? What is the length? What fraction of a wavelength is present? 3. Suppose you wanted to select a string for a piano that would have a fundamental frequency of 64 Hz (2 octaves below middle C). The speed of the wave in this string is 95 m/s. Calculate the shortest length for this string. Confirm by simulation. 4. Calculate the 2nd and 3ªd harmonic frequencies for the string above. 5. Uncheck “closed/open tube" so that you now have a tube with the right end open. (Keep the wave speed at 40 m/s.) For fundamental frequency of 20 Hz, calculate the length of the tube. Calculate the frequencies of the next two overtones and corresponding wavelengths for this tube. Confirm resonances in simulation.
wave speed (m/s) 35 Closed/Open Tube frequency (Hz) 60 0.032 simulation speed start stop 4 reset length of tube (m) 3.3
Transcribed Image Text:wave speed (m/s) 35 Closed/Open Tube frequency (Hz) 60 0.032 simulation speed start stop 4 reset length of tube (m) 3.3
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