Speed of propagation of sound wave?

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SUMMARY

The speed of propagation of sound waves in the inner ear can be calculated using the equation frequency = velocity / wavelength. In this discussion, the lowest frequency of 20 Hz corresponds to a wavelength of 4.5 m, leading to an initial calculation of sound wave velocity at 2.4 m/s. However, this value is incorrect as it does not align with the expected propagation speed in biological tissues. The correct approach involves understanding the relationship between frequency and wavelength in the context of sound transmission through the basilar membrane.

PREREQUISITES
  • Understanding of sound wave properties, including frequency and wavelength
  • Familiarity with the equation f = v/λ (frequency = velocity / wavelength)
  • Basic knowledge of the anatomy of the inner ear, particularly the basilar membrane
  • Concept of harmonic series in musical notes and their frequency ratios
NEXT STEPS
  • Research the speed of sound in biological tissues and its implications for auditory processing
  • Explore the harmonic series and its mathematical representation in sound frequencies
  • Learn about the anatomy and function of the basilar membrane in sound perception
  • Investigate the effects of frequency ratios on sound wave propagation in different media
USEFUL FOR

Students studying acoustics, audiology professionals, and anyone interested in the physics of sound and its biological implications.

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Homework Statement


Assume a piano has 100 different notes from the lowest to highest. We go up from note to note by the same frequency ratio, say starting at 20 Hz. Assuming that the lowest frequency excites the basilar membrane, 30 mm long, at its end, and that this represents a quarter of a wavelength.

What is the speed of propagation of the sound wave in the inner ear?


Homework Equations


Frequency = velocity / wavelength (?)

The Attempt at a Solution


My attempt at the solution resulted in a velocity of 2.4 m/s, but I'm sure that I'm using the wrong equation.
 
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I started by calculating the wavelength of the lowest frequency, which would be 4.5 m. Then I calculated the frequency of the highest note, which would be 2000 Hz. Next, I used the equation f = v/λ which gave me a velocity of 2.4 m/s. But I'm not sure if this is the correct equation to use and if my answer is correct.
 

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