Opera singer and crystal goblet

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To shatter a crystal goblet through resonance, an opera singer must produce a frequency that matches the goblet's natural frequency. Given the rim's circumference of 10.6 cm and the presence of four nodes and antinodes, the wavelength can be calculated as the circumference divided by the number of nodes (or antinodes). Using the wave speed of 900 m/s, the relationship between wave speed, wavelength, and frequency (v = fλ) can be applied to find the required frequency. The final frequency needed to resonate and potentially shatter the glass is determined in kilohertz (kHz). Understanding these principles allows for solving the problem effectively.
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Standing-wave vibrations are set up in a crys-
tal goblet with four nodes and four antinodes
equally spaced around the 10:6 cm circumfer-
ence of its rim.
If transverse waves move around the glass
at 900 m=s, an opera singer would have to
produce a high harmonic with what frequency
in order to shatter the glass with a resonant
vibration? Answer in units of kHz.

I'm stuck on this problem, please help.
 
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If the rim has a wave with 4 nodes and 4 antinodes then what is the wavelength of that wave considering the rim is 10.6cm? Since you are given the wave speed do you know of any equation that relates the wave speed the wavelength and the frequency?
 

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