Question

An experimenter wishes to generate in air a sound wave that has a displacement amplitude of 5.50 * 10²⁶ m. The pressure amplitude is to be limited to 0.840 Pa. What is the minimum wavelength the sound wave can have?

Answer 1

The minimum wavelength of a sound wave can be calculated using the equation: λ = v / f, where λ is the wavelength, v is the speed of sound, and f is the frequency of the wave. In this case, we are given the pressure amplitude (Ap) and the displacement amplitude (Ad) of the wave. The pressure amplitude can be related to the displacement amplitude using the equation Ap = α × Ad, where α is the speed of sound in air. Substituting this relationship into the equation for wavelength gives: λ = v / (Ap / (α × Ad)). Plugging in the values, we can calculate the minimum wavelength.

Step-by-step explanation:

The minimum wavelength of a sound wave can be calculated using the equation:

λ = v / f

where λ is the wavelength, v is the speed of sound, and f is the frequency of the wave.

In this case, we are given the pressure amplitude (Ap) and the displacement amplitude (Ad) of the wave. The pressure amplitude can be related to the displacement amplitude using the equation:

Ap = α × Ad

where α is the speed of sound in air.

Substituting this relationship into the equation for wavelength gives:

λ = v / (Ap / (α × Ad))

Plugging in the values, we can calculate the minimum wavelength.