Asinusoidal wave has the following wave function: y(x, t) = (2.5 m) sin[(3.0 m-1) x – (24 s-1) t + π/2] what is the frequency of this wave?

3.82 Hertz

Explanation:

This is the equation of a wave which varies sinusoidally.

The standard equation of a wave is given by

where, A be the amplitude of the wave, k be the wave number, x be the displacement of wave, ω be the angular frequency and t be the time taken, and Ф be the phase angle.

now compare the given equation by the standard equation, we get

k = 3

ω = 24

Ф = π / 2

So, the angular frequency = 24

The relation between the angular frequency and the frequency is given by

ω = 2 x π x f

24 = 2 x 3.14 x f

f = 3.82 Hertz

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i just did this and got a 100.

we have been given a quadratic function and we need to restrict the domain such that it becomes a one to one function.

we know that vertex of this quadratic function occurs at (5,2).

further, we know that range of this function is .

if we restrict the domain of this function to either or , it will become one to one function.

let us know find its inverse.

upon interchanging x and y, we get:

let us now solve this function for y.

hence, the inverse function would be if we restrict the domain of original function to and the inverse function would be if we restrict the domain to .