Speed of propagation of sound wave?

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The discussion focuses on calculating the speed of sound propagation in the inner ear based on a piano's frequency range. The user initially calculates the wavelength for the lowest frequency of 20 Hz, resulting in 4.5 m, and then determines the highest note's frequency to be 2000 Hz. Using the equation f = v/λ, they arrive at a velocity of 2.4 m/s but express uncertainty about the correctness of their approach. The conversation highlights the importance of using the correct equations and understanding wave properties in sound propagation. Clarification on the appropriate formulas and calculations is sought to verify the results.
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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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