Question:

A sound wave travels through air with a frequency of 2000 Hz and a wavelength of 0.5 meters. The speed of sound in air is 343 m/s. Determine:

a) The period of the sound wave.

b) The amplitude of the sound wave.

c) The wave speed of the sound wave.

d) The equation of the sound wave in terms of displacement as a function of time.

e) Determine if this sound wave is audible to the human ear.

Answer:

a) The period of a sound wave is the time it takes for one complete cycle. It can be calculated using the formula T = 1/frequency.

Given frequency (f) = 2000 Hz

Using the formula, T = 1 / f

T = 1 / 2000 = 0.0005 seconds

Therefore, the period of the sound wave is 0.0005 seconds.

b) The amplitude of a sound wave represents the maximum displacement of particles from their equilibrium position. In this question, no information about the amplitude is provided. Hence, it cannot be determined with the given data.

c) The wave speed is determined by the formula v = λf, where v is the wave speed, λ is the wavelength, and f is the frequency.

Given wavelength (λ) = 0.5 meters Given frequency (f) = 2000 Hz

Using the formula, v = λ * f

v = 0.5 * 2000 = 1000 m/s

Therefore, the wave speed of the sound wave is 1000 m/s.

d) The equation of the sound wave, represented as displacement as a function of time, is given by the formula:

y(x, t) = A * sin(2πf * t - 2πx / λ)

Where: y(x, t) is the displacement at position x and time t, A is the amplitude of the wave (which is not given), f is the frequency of the wave, t is the time, and λ is the wavelength of the wave.

Since the amplitude of the wave is not provided, the equation cannot be determined with the given data.

e) In general, the human ear can detect sound waves within a frequency range of approximately 20 Hz to 20,000 Hz. Since the given frequency of the sound wave is 2000 Hz, it falls within the audible range for the human ear.

Hence, this sound wave is audible to the human ear.