3. The vocal tract tube measures approximately 20 cm (0.2 meters) in length. What would be the 3d mode of vibration during production of a vowel with an open mouth posture. Use formula for 1/4 wave resonator and c=343 m/sec (velocity for sound transmission in air).

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Author:Raymond A. Serway, John W. Jewett
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Chapter15: Oscillatory Motion
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I need help with #3-5 thank you!

1. Using a 2 meter long slinky that is anchored on both ends, what is the frequency of the 2nd mode of
vibration, given a velocity of c = 500 m/sec.
2. Using a 1 meter long slinky that is anchored at only one end, what is the frequency for the 1st mode
of vibration, given a velocity of c = 500 m/sec.
3. The vocal tract tube measures approximately 20 cm (0.2 meters) in length. What would be the 3rd
mode of vibration during production of a vowel with an open mouth posture. Use formula for 1/4
wave resonator and c=343 m/sec (velocity for sound transmission in air).
4. You pick up an empty 16 oz. plastic coke bottle and blow a steady airstream over the top edge of the
bottle's mouth to set the air in the bottle into resonance. What is the frequency of the 1" mode for the
bottle? (Hint: you'll need a metric ruler for this question).
5. The Empire State Building in NYC is approximately 440 meters in height. The superstructure of the
building is made of steel which means that energy will be transmitted through the buildings core at 1500
m/sec. If the building is being blasted and buffeted by a strong wind storm, at what frequency will the
building sway in it's 1st mode of vibration. (Hint: think about what type of a resonator a building could be)
Transcribed Image Text:1. Using a 2 meter long slinky that is anchored on both ends, what is the frequency of the 2nd mode of vibration, given a velocity of c = 500 m/sec. 2. Using a 1 meter long slinky that is anchored at only one end, what is the frequency for the 1st mode of vibration, given a velocity of c = 500 m/sec. 3. The vocal tract tube measures approximately 20 cm (0.2 meters) in length. What would be the 3rd mode of vibration during production of a vowel with an open mouth posture. Use formula for 1/4 wave resonator and c=343 m/sec (velocity for sound transmission in air). 4. You pick up an empty 16 oz. plastic coke bottle and blow a steady airstream over the top edge of the bottle's mouth to set the air in the bottle into resonance. What is the frequency of the 1" mode for the bottle? (Hint: you'll need a metric ruler for this question). 5. The Empire State Building in NYC is approximately 440 meters in height. The superstructure of the building is made of steel which means that energy will be transmitted through the buildings core at 1500 m/sec. If the building is being blasted and buffeted by a strong wind storm, at what frequency will the building sway in it's 1st mode of vibration. (Hint: think about what type of a resonator a building could be)
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