The variation in the pressure of helium gas,measured from its equilibrium value,is given by $\Delta$P = 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 the speed of a wave is:
v = λ f
where v is the wave speed in m/s, λ is the wavelength in meters, and f is the frequency in Hz.
In the given equation, we can see that the term inside the cosine function represents the angular frequency (ω) of the wave:
ω = 6.20x × 3000 = 18.6x × 10^3
The wavelength can be found from the equation:
λ = 2π/k
where k is the wave number, which is related to the angular frequency by:
k = ω/v
Substituting the given values, we get:
k = (18.6x × 10^3) / v
and
λ = 2π / [(18.6x × 10^3) / v]
Simplifying, we get:
λ = (2πv) / (18.6x × 10^3)
Comparing this with the given equation for pressure variation, we can see that x = λ/2.
Therefore, substituting for λ, we get:
x = πv / (18.6x × 10^3)
Solving for v, we get:
v = (π / 18.6) × (x / t)
Substituting the given values, we get:
v = (π / 18.6) × (484 / 3000) = 83.4 m/s
Therefore, the closest answer choice is C) 484 m/s.

The Variation in the Pressure of Helium Gas,measured from Its Δ\DeltaΔ

The Variation in the Pressure of Helium Gas,measured from Its $\Delta$