Question

A sinusoidal sound wave moves through a medium and is described by the displacement wave function

Answer 1

By applying the wave equation we know that the speed of wave is 54.6 m/s.

We need to know about wave equations to solve this problem. The displacement of the wave on the y-axis can be explained by the wave equation

y = A cos (kx - ωt)

where y is y-axis displacement, A is amplitude, k is wave number, x is x-axis displacement, ω is angular speed and t is time.

the wavenumber and angular speed of the wave equation can be determined respectively by

k = 2π / λ

ω = 2πf

where k is the wavenumber, λ is wavelength and f is frequency.

From the question above, we know that:

y = 2.00cos (15.7x - 858t)

By applying the wave equation, we know that

ω = 858 rad/s

k = 15.7 /m

Find the frequency of the wave

ω = 2πf

858 = 2π . f

f = 136.5 Hz

Find the wavelength

k = 2π / λ

15.7 = 2π / λ

λ = 0.40 meters

Calculate the speed of wave

v = λ . f

v = 0.40 x 136.5

v = 54.6 m/s

For more on wave equation on: brainly.com/question/25699025

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