The equation of a progressive wave is generally given by y(x, t) = A sin(ωt - kx + φ), where:

- A is the amplitude of the wave
- ω is the angular frequency
- k is the wave number
- φ is the phase constant

Comparing this with the given equation y(x, t) = 2sin(πt - πx), we can identify the following:

(a) The angular frequency (ω) is the coefficient of t in the argument of the sine function. Here, ω = π rad/s.

(b) The wave number (k) is the coefficient of x in the argument of the sine function. Here, k = π rad/cm. The wavelength (λ) is given by 2π/k, so λ = 2 cm.

(c) The period (T) of the wave is the reciprocal of the frequency, and the frequency (f) is ω/2π. So, f = ω/2π = π rad/s / 2π = 0.5 Hz. Therefore, T = 1/f = 1/0.5 = 2 s.

(d) The wave speed (v) is given by the product of the wavelength and the frequency, so v = λf = 2 cm * 0.5 Hz = 1 cm/s.

Question

The equation of a progressive wave is generally given by y(x, t) = A sin(ωt - kx + φ), where:

- A is the amplitude of the wave
- ω is the angular frequency
- k is the wave number
- φ is the phase constant

Comparing this with the given equation y(x, t) = 2sin(πt - πx), we can identify the following:

(a) The angular frequency (ω) is the coefficient of t in the argument of the sine function. Here, ω = π rad/s.

(b) The wave number (k) is the coefficient of x in the argument of the sine function. Here, k = π rad/cm. The wavelength (λ) is given by 2π/k, so λ = 2 cm.

(c) The period (T) of the wave is the reciprocal of the frequency, and the frequency (f) is ω/2π. So, f = ω/2π = π rad/s / 2π = 0.5 Hz. Therefore, T = 1/f = 1/0.5 = 2 s.

(d) The wave speed (v) is given by the product of the wavelength and the frequency, so v = λf = 2 cm * 0.5 Hz = 1 cm/s.

Knowee AI · Accepted Answer

The equation of a progressive wave is generally given by y(x, t) = A sin(ωt - kx + φ), where:

- A is the amplitude of the wave
- ω is the angular frequency
- k is the wave number
- φ is the phase constant

Comparing this with the given equation y(x, t) = 2sin(πt - πx), we can identify the following:

(a) The angular frequency (ω) is the coefficient of t in the argument of the sine function. Here, ω = π rad/s.

(b) The wave number (k) is the coefficient of x in the argument of the sine function. Here, k = π rad/cm. The wavelength (λ) is given by 2π/k, so λ = 2 cm.

(c) The period (T) of the wave is the reciprocal of the frequency, and the frequency (f) is ω/2π. So, f = ω/2π = π rad/s / 2π = 0.5 Hz. Therefore, T = 1/f = 1/0.5 = 2 s.

(d) The wave speed (v) is given by the product of the wavelength and the frequency, so v = λf = 2 cm * 0.5 Hz = 1 cm/s.

A progressive wave is represented by the equation𝑦(𝑥, 𝑡) = 2sin⁡(𝜋𝑡 − 𝜋𝑥)where y and x are in centimeters and t in seconds.(a) Determine the angular frequency, the wavelength, the period, the frequency and thewave speed

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