A 50 -cm-long wire with a mass of 1.0 g and a tension of 440 N passes across the open end of a

step 1 a 50 cm long wire with a mass of RAM and tension of 440 Newton pass across open end of an open c

A 50 -cm-long wire with a mass of 1.0 g and a tension of...

A 50 -cm-long wire with a mass of $1.0 \mathrm{~g}$ and a tension of $440 \mathrm{~N}$ passes across the open end of an open-closed tube of air. The wire, which is fixed at both ends, is bowed at the center so as to vibrate at its fundamental frequency and generate a sound wave. Then the tube length is adjusted until the fundamental frequency of the tube is heard. What is the length of the tube? Assume the speed of sound is $340 \mathrm{~m} / \mathrm{s}$.

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Vibrating String Fundamentals

The fundamental frequency of a vibrating string fixed at both ends is determined by the formula f = (1/2L)?(T/?), where L is the length of the string, T is the tension, and ? is the linear mass density. This concept explains how the physical properties of the string influence the pitch of the sound it produces.

Linear Mass Density

Linear mass density, ?, is defined as the mass per unit length of a string or wire. It is a crucial parameter when calculating the speed of wave propagation along the string, as it directly affects the fundamental frequency through the relation between tension and mass distribution.

Acoustic Resonance in Open-Closed Tubes

In open-closed tubes, the fundamental frequency is related to the speed of sound and the length of the tube by the formula f = v/(4L), where v is the speed of sound. This principle is used to determine the resonant frequencies of the air column, which are essential for matching the frequency produced by the vibrating string to that of the air column.

Transcript

Please give Ace some feedback