What is the frequency of a sound wave traveling through air in a tube?

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SUMMARY

The frequency of a sound wave traveling through air in a tube can be determined using the wave equation and the properties of sound. Given the wave equation s = sm cos(kx - ωt + φ) and the speed of sound at 347 m/s, the frequency can be calculated using the relationship between wave speed, wavelength, and frequency. The maximum positive displacement of air molecules A and B indicates the amplitude of the wave, which is essential for understanding sound wave behavior. The solution requires knowledge of wave properties and the relationship between displacement and frequency.

PREREQUISITES
  • Understanding of wave equations, specifically s = sm cos(kx - ωt + φ)
  • Knowledge of sound wave properties, including speed and displacement
  • Familiarity with the concept of frequency and its calculation
  • Basic physics principles regarding oscillation and wave propagation
NEXT STEPS
  • Learn how to calculate frequency from wave speed and wavelength
  • Study the relationship between amplitude and energy in sound waves
  • Explore the concept of wave interference and its effects on sound
  • Investigate the behavior of sound waves in different mediums
USEFUL FOR

Students studying physics, particularly those focusing on wave mechanics and sound properties, as well as educators seeking to explain sound wave behavior in a practical context.

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Homework Statement


A sound wave of the form s = sm cos(kx - ωt + φ) travels at 347 m/s through air in a long horizontal tube. At one instant, air molecule A at x = 2.04 m is at its maximum positive displacement of 6.40 nm and air molecule B at x = 2.08 m is at a positive displacement of 2.10 nm. All the molecules between A and B are at intermediate displacements. What is the frequency of the wave?


Homework Equations





The Attempt at a Solution


uhhh I'm pretty much confused from the get go...i'm not sure how air molecules interact with a wave? i might need to be spoon fed a little here, because i don't even know where to start! ANY HINTS GREATLY APPRECIATED :)
 
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Sound is basically the vibration of air molecules: as molecules oscillate, they force their neighbors into the same type of motion. Sound being a wave, some air molecules vibrate more than others, like how the middle of a guitar string vibrates more than the string's ends. Need any more hints?
 
ahhh sorry yea, i have NO idea...didn't even know the middle of a guitar string vibrates more than the ends (and totally don't know why)...
 

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