High-frequency sound can be used to produce standing-wave vibrations in a wine g

Question

High-frequency sound can be used to produce standing-wave vibrations in a wine glass. A standing-wave vibration in a wine glass is observed to have four nodes and four antinodes equally spaced around the 10.0-cm circumference of the rim of the glass. If transverse waves move around the glass at 905 m/s, an opera singer would have to produce a high harmonic with what frequency to shatter the glass with a resonant vibration as shown in the figure below?
kHz

High-frequency sound can be used to produce standing-wave vibrations in a wine glass. A standing-wave vibration in a wine glass is observed to have four nodes and four antinodes equally spaced around the 10.0-cm circumference of the rim of the glass. If transverse waves move around the glass at 905 m/s, an opera singer would have to produce a high harmonic with what frequency to shatter the glass with a resonant vibration as shown in the figure below?

Explanation / Answer

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

? = Circumference / 4 * 2

? = 0.10 / 2
= 0.5 m

Given the speed of the traverse wave at resonant frequency is 900 m/s, for frequency:
f = v/?

f = 905 / 0.5
= 1810 Hz

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