   Chapter 14, Problem 52P

Chapter
Section
Textbook Problem

Standing-ware vibrations are set up in a crystal goblet with four nodes and four antinodes equally spaced around the 20.0-cm circumference 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?

To determine
The frequency of the sound in order to shatter glass with a resonant vibration.

Explanation

Given Info: The circumference of the rim is 20.0cm .

The distance between adjacent nodes and between adjacent antinodes is equal to one quarter of the circumference, so that.

d=d4

• d is the circumference of the rim,
• d is the distance between adjacent nodes and antinodes,

Substitute 20.0cm for d to find d .

d=20.0cm4=5.00cm

Formula to calculate the wavelength of the standing wave is,

λ=2d

• λ is the wavelength,

Substitute 5.00cm for d to find λ

λ=2(5.00cm)=10.0cm

Thus, the wavelength of the standing wave is 10

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