Answer:13394.15 m
Step-by-step 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.