Speed of propagation of sound wave?

In summary, the conversation discusses the calculation of the speed of sound propagation in the inner ear. It assumes a piano with 100 notes and a frequency ratio of 20 Hz. The lowest frequency is assumed to excite the basilar membrane, which is 30 mm long. Using the equation f = v/λ, the speaker attempted to calculate the velocity and arrived at a value of 2.4 m/s, but is unsure if this is the correct equation and answer.
  • #1
whitestork
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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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  • #2
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.
 

What is the speed of sound?

The speed of sound is the distance that a sound wave travels in a unit of time. It is typically measured in meters per second (m/s). In dry air at 20°C, the speed of sound is approximately 343 m/s.

How does the speed of sound vary in different mediums?

The speed of sound varies depending on the medium it is traveling through. In general, sound travels faster in denser mediums, such as solids, and slower in less dense mediums, such as gases. For example, sound travels at about 1,500 m/s in water and 3,300 m/s in steel.

What factors affect the speed of sound?

The speed of sound is affected by the temperature, humidity, and density of the medium it is traveling through. It is also influenced by the elasticity and compressibility of the medium. In addition, the speed of sound can be affected by external factors such as wind and air pressure.

How does the speed of sound change with temperature?

In general, the speed of sound increases with higher temperatures. This is because as the temperature increases, the molecules in the medium vibrate more rapidly, allowing sound waves to travel faster. However, this relationship is not linear and can vary depending on the specific medium and conditions.

Why is the speed of sound faster in solids than in gases?

Sound waves travel faster in solids because the molecules in solids are packed closer together, allowing the sound waves to travel more quickly. In gases, the molecules are more spread out, resulting in a slower speed of sound. This is also why sound waves can travel longer distances in solids than in gases.

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