High School

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A wave has a frequency of [tex]2.79 \times 10^3[/tex] Hz and an angular wave number of [tex]37.6[/tex] rad/m. How far will the wave travel in [tex]28.7[/tex] seconds?

Answer :

Answer:13394.15 m

Explanation:

We can use the wave speed formula to solve this problem. The wave speed (v) of a wave is given by the product of its frequency (f) and wavelength (λ):

v = fλ

The angular wave number (k) is related to the wavelength by the formula:

k = 2π/λ

So we can rearrange the formulas to get:

λ = 2π/k

and

v = fλ = f(2π/k)

Substituting the given values, we get:

λ = 2π/37.6 rad/m = 0.167 m

v = (2.79 x 10^3 Hz)(0.167 m) = 466.93 m/s

Finally, we can use the formula for distance (d) traveled by a wave in time (t) to get:

d = vt = (466.93 m/s)(28.7 s) = 13394.15 m

Therefore, the wave will travel approximately 13394.15 meters in 28.7 seconds.

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