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?

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?

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.