Question

When responding to sound, the human eardrum vibrates about its equilibrium position. Suppose an eardrum is vibrating with an amplitude of 5.0 x10-7 m and a maximum speed of 3.3 x10-3 m/s. (a) What is the frequency (in Hz) of the eardrum's vibrations? (b) What is the maximum acceleration of the eardrum?

Answer 1

When responding to sound, the human eardrum vibrates about its equilibrium position. Suppose an eardrum is vibrating with an amplitude of 5.0 x10-7 m and a maximum speed of 3.3 x10-3 m/s. (a) What is the frequency (in Hz) of the eardrum's vibrations? (b) What is the maximum acceleration of the eardrum?

Answer 2

[AI-generated answer — Explain Bot]

To find the frequency of the eardrum's vibrations, we can use the formula:

Frequency (f) = Speed (v) / Wavelength (λ)

In this case, the speed is the maximum speed of the eardrum, which is given as 3.3 x 10^(-3) m/s. The wavelength can be calculated using the formula:

Wavelength (λ) = 2 * Amplitude (A)

Substituting the values, we have:

Wavelength (λ) = 2 * 5.0 x 10^(-7) m = 1.0 x 10^(-6) m

Now, we can calculate the frequency:

Frequency (f) = 3.3 x 10^(-3) m/s / 1.0 x 10^(-6) m = 3.3 x 10^3 Hz

So, the frequency of the eardrum's vibrations is 3.3 x 10^3 Hz.

To find the maximum acceleration of the eardrum, we can use the formula:

Acceleration (a) = (2π * Frequency (f))^2 * Amplitude (A)

Substituting the values:

Acceleration (a) = (2π * 3.3 x 10^3 Hz)^2 * 5.0 x 10^(-7) m = 1.72 x 10^3 m/s^2

Therefore, the maximum acceleration of the eardrum is 1.72 x 10^3 m/s^2.