Answer:
a) The pressure in a traveling sound wave is given by the equation
p Pa π m x s t − − Δ = −
s x, t 6.0 nm cos kx+ 3000 rad / s t+ ( )( ) ( ) ( )
Find the (a) pressure amplitude, (b) frequency, (c) wavelength,
and (d) speed of the wave.
b) If the form of a sound wave traveling through air is
= ϕ , how much time does any given air molecule along
the path take to move between displacements s = + 2.0 nm and s = - 2.0 nm?
Solution: (a) The amplitude of a sinusoidal wave is the numerical coefficient of the sine (or
cosine) function: pm = 1.50 Pa.
We identify k = 0.9π and ω = 315 π (in SI units), which leads to f = ω /2 π = 158 Hz.
We also obtain λ = 2π/k = 2.22 m.
The speed of the wave is v = λ /k = 350 m/s.
(b) Without loss of generality we take x = 0, and let t = 0 be when s = 0. This means the
phase is φ= -π/2 and the function is s = (6.0 nm)sin(ωt) at x = 0. Noting that ω = 3000 rad/s,
we note that at t = sin-1(1/3)/ω = 0.1133 ms the displacement is s = +2.0 nm. Doubling that
time (so that we consider the excursion from –2.0 nm to +2.0 nm) we conclude that the time
required is 2(0.1133 ms) = 0.23 ms.