The variation in the pressure of helium gas, measured from its equilibrium value, is given by ΔP = 2.9 × 10−⁵ cos (6.20x − 3 000t) where x and t have units m and s. Determine the speed (in m/s) of the wave. A) 1 515 B) 153 C) 484 D) 828 E) 101

Question

Quizplus · Accepted Answer

The general equation for a wave is: ΔP = A sin(kx − ωt) where A is the amplitude, k is the wave number, x is the position, ω is the angular frequency, and t is the time. We can see that the given equation has a cosine instead of a sine, but this is not a problem because a cosine is just a shifted sine. Comparing the given equation with the general equation, we can see that: A = 2.9 × 10−⁵ k = 6.20 ω = 3 000 The speed of the wave is given by: v = ω/k Substituting the values, we get: v = 3 000/6.20 = 484 m/s Therefore, the correct answer is C.

The Variation in the Pressure of Helium Gas, Measured from Its