The Resonant Wine Cellar · AI Generator #GEN-13BB0F2E

Physics

Problem

A wine enthusiast notices that when trucks pass by her underground wine cellar, certain wine bottles produce a clear humming sound. The cellar is carved into limestone bedrock and has a rectangular cross-section that is

2.4\;\text{m}

wide and

3.2\;\text{m}

high. The cellar extends

15\;\text{m}

into the hillside and is open only at the entrance. When a truck with a dominant engine frequency of

85\;\text{Hz}

passes overhead, the cellar resonates strongly and bottles hum in sympathy. The speed of sound in the cool cellar air is

330\;\text{m/s}

. (a) What is the wavelength of the sound wave that causes this resonance? (b) The cellar acts as a three-dimensional resonant cavity. Determine which resonant mode (characterized by integers

m

n

, and

p

for the three spatial dimensions) is being excited by the truck. (c) If the cellar temperature drops and the speed of sound decreases to

320\;\text{m/s}

, what engine frequency would now cause the same resonant mode to be excited?

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