Crystal Goblet-Opera Singer Frequency Problem

AI Thread Summary
To shatter a crystal goblet through resonant vibration, an opera singer must produce a frequency that matches the goblet's natural frequency, determined by its dimensions and the speed of sound in the glass. The goblet has four nodes and four antinodes, indicating a specific harmonic mode. The relationship between wave speed, frequency, and wavelength is crucial, with the formula V=F*wavelength guiding the calculations. Understanding how nodes and antinodes relate to wavelength is essential for determining the correct frequency needed to achieve resonance. Accurate calculations are necessary to avoid failure in the final attempt.
pc21
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Homework Statement



Standing-wave vibrations are set up in a crystal goblet with four nodes and four antinodes equally spaced around the 15.0 cm circumference of its rim. If transverse waves move around the glass at 920 m/s, an opera singer would have to produce a high harmonic with what frequency to shatter the glass with a resonant vibration?


Homework Equations



V=F*wavelength

The Attempt at a Solution


if someone could explain how to do this or do it out it would be good because i have one more chance to get it right otherwise its wrong
 
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Hi pc21,

How are the nodes and antinodes related to the wavelength of a wave?
 

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