Crystal Goblet-Opera Singer Frequency Problem

[pc21]

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

 

[alphysicist]

Hi pc21,

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

 

[Moetasim]

I would approach this problem by first understanding the concept of resonance and how it relates to standing waves. Resonance occurs when a system is driven at its natural frequency, resulting in a large amplitude oscillation. In this case, the crystal goblet is acting as the resonant system and the opera singer's voice is providing the driving force.

To calculate the frequency that the opera singer would need to produce in order to shatter the glass, we can use the formula V = fλ, where V is the velocity of the transverse waves (920 m/s), f is the frequency, and λ is the wavelength.

Since the crystal goblet has four nodes and four antinodes equally spaced around its circumference, we can assume that the wavelength of the standing wave is equal to the circumference of the goblet (15.0 cm). This means that λ = 15.0 cm = 0.15 m.

Substituting this value into the formula, we can solve for the frequency: f = V/λ = (920 m/s)/(0.15 m) = 6133.33 Hz.

Therefore, the opera singer would need to produce a high harmonic with a frequency of 6133.33 Hz in order to shatter the glass with a resonant vibration. It is important to note that this is a theoretical calculation and many factors, such as the thickness and material of the glass, could affect the actual frequency needed to shatter the glass.