Write the equation of a wave, traveling along the +x axis with an amplitude of 0.02 m, a frequency of 440 Hz, and a speed of 330 m/sec.
A) y = 0.02 sin [880π(x/330 − t)]
B) y = 0.02 cos [880π x/330 − 440t]
C) y = 0.02 sin [880π(x/330 + t)]
D) y = 0.02 sin [2π(x/330 + 440t)]
E) y = 0.02 cos [2π(x/330 + 440t)]

Question

Quizplus · Accepted Answer

The general equation for a wave traveling along the +x axis can be written as y = A sin(kx − ωt + φ), where A is the amplitude, k is the wave number (2π/λ), ω is the angular frequency (2πf), t is time, and φ is the phase angle. Using the given values, we have:

A = 0.02 m
f = 440 Hz
v = 330 m/sec
λ = v/f = 330/440 = 0.75 m
k = 2π/λ = 8.38 m^−1
ω = 2πf = 880π rad/sec

Substituting these values into the general equation, we get:

y = 0.02 sin(8.38x − 880πt)

This matches with the equation given in choice A, y = 0.02 sin [880π(x/330 − t)]. Therefore, the answer is A.

Write the Equation of a Wave, Traveling Along the +X