Question

Consider the following wave function in SI units:

ΔP(x,t) = (24.0 / r) sin(1.35r - 2050t)
Include answers to such questions as the following and give representative values for any quantities that can be evaluated. (Assume that the wave is moving through the water at 25°C.)
(a) Does the wave move more toward the right or the left?
(b) Find its wavelength.
(c) Find its speed.
(d) Find its frequency.

Answer 1

(a) right

(b) λ = 4.65m

(c) v = 1519m/s

(d) f = 327Hz

Step-by-step explanation:

The characteristic sinusoidal pressure fluctuation equation for a wave traveling to the right is given as

P(x,t) = BkASin(kx-ωt)

Where

B = Bulk modulus

k = wave number

A = displacement amplitude

x = position on the x-axis

ω = angular frequency

t = time t

(a) the wave is travelling to the right

(b) from the given equation

ΔP(x,t) = (24.0 / r) sin(1.35r - 2050t)

1.35 compares with k

So k = 1.35rad/m

And k = 2π/ λ

λ = 2π/k = 2π/1.35 = 4.65m

(c) ω =kv

From the given equation ω = 2050 rad/s

v = ω/k = 2050/1.35 = 1519m/s

(d) f = v/λ =1519/4.65 = 327Hz