Question

A wave is represented by Ψ = 3x10-3cos(8.4 x 1013 t+2.8 x 105 Z) Vm -1.
Find the amplitude, frequency, wavelength, and wave velocity where ‘z’ in meter
and ‘t’ in second.

Answer 1

Answer:

jjfoto A wave is represented by Ψ = 3x10-3cos(8.4 x 1013 t+2.8 x 105 Z) Vm -1.

Find the amplitude, frequency

Explanation:

A wave is represented by Ψ = 3x10-3cos(8.4 x 1013 t+2.8 x 105 Z) Vm -1.

Find the amplitude, frequency

Answer 2

AMPLITUDE - 3x10^-3 Vm^-1

FREQUENCY - 1.34 x 10^13 Hz

WAVELENGTH - 22.4 x 10^-6 m or 22.4 micrometers

WAVE VELOCITY -  3 x 10^8 m/s

Given,

Ψ = 3x10^-3cos(8.4 x 10^13 t + 2.8 x 10^5 Z) Vm^-1

To find,

The amplitude, frequency, wavelength, and wave velocity.

Solution,

From the given equation we found,

The amplitude, A = 3x10^-3 Vm^-1

The angular frequency, ω = 8.4 x 10^13 rad/s

The wavenumber, k = 2.8 x 10^5 m^-1

Formulae used for calculating:

• Frequency (f) = ω/2π
• Wavelength (λ) = 2π/k
• Wave velocity (v) = λf

Further calculations,

Frequency (f) = ω/2π = (8.4 x 10^13 rad/s)/(2π) ≈ 1.34 x 10^13 Hz

Wavelength (λ) = 2π/k = 2π/(2.8 x 10^5 m^-1) ≈ 22.4 x 10^-6 m or 22.4 micrometers

Wave velocity (v) = λf = (22.4 x 10^-6 m) x (1.34 x 10^13 Hz) ≈ 3 x 10^8 m/s (approximately the speed of light in a vacuum)

Therefore, the amplitude of the wave is 3x10^-3 Vm^-1, the frequency is approximately 1.34 x 10^13 Hz, the wavelength is approximately 22.4 micrometers, and the wave velocity is approximately 3 x 10^8 m/s.

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