Question

A loud factory machine produces sound having a displacement amplitude in air of 1.00 μm, but the frequency of this sound can be adjusted. In order to prevent ear damage to the workers, the maximum pressure amplitude of the sound waves is limited to 10.0 Pa. Under the conditions of this factory, the bulk modulus of air is 1.31×105 Pa. The speed of sound in air is 344 m/s. What is the highest-frequency sound to which this machine can be adjusted without exceeding the prescribed limit?

Answer 1

Answer:

f = 4179.33  Hz

Explanation:

given,

Pressure = 10 Pa

bulk modulus of air = 1.31 × 10⁵ Pa

speed of sound = 344 m/s

displacement amplitude = 10⁻⁶ m

using formula

$P_{max}=B(\dfrac{2 \pi f}{v})A$

$f = \dfrac{P_{max}V}{2\pi BA}$

$f = \dfrac{10\times 344}{2\pi \times 1.31 \times 10^5\times 10^{-6}}$

f = 4179.33  Hz

the highest frequency of the sound to machine is f = 4179.33  Hz