Question

A wine glass can be shattered by establishing a standing wave vibration of high frequency around the rim of the glass. What is the frequency of such a sound (in kHz) if it establishes four nodes and four antinodes equally spaced around the 28.0 cm circumference of the rim of the glass and has a speed of 4,260 m/s?

Answer 1

The wave travels along the circumference of glass, has 4 nodes. This means, it has two complete phases (wavelengths) over it:

Wavelength λ= Circumference / 4 * 2

Circumference = 4 * 28 cm
In this case:

λ = 0.28 / 2
= 0.14 m

Given the speed of the traverse wave at resonant frequency is 4,260 m/s, we can solve for frequency:
f = v/λ

v is velocity of wave , f is frequency

f = 4260 / 0.14
= 30428.5 Hz
= 30.4  KHz

Frequency of such sound f is 30.4 KHz