Answer
(a) The maximum velocity and maximum acceleration are greatest for high-frequency sounds.
(b) The maximum velocity is $1.26\times 10^{-16}~m/s$
The maximum acceleration is $1.58\times 10^{-14}~m/s^2$
(c) The maximum velocity is $1.26\times 10^{-13}~m/s$
The maximum acceleration is $1.58\times 10^{-8}~m/s^2$
Work Step by Step
(a) We can write an expression for the maximum velocity:
$v_m = A~\omega = A~(2\pi~f)$
We can write an expression for the maximum acceleration:
$a_m = A~\omega^2 = A~(2\pi~f)^2$
We can see that the maximum velocity and maximum acceleration are greatest for high-frequency sounds.
(b) We can find the maximum velocity:
$v_m = A~\omega$
$v_m = A~(2\pi~f)$
$v_m = (1.0\times 10^{-18}~m)~(2\pi)~(20.0~Hz)$
$v_m = 1.26\times 10^{-16}~m/s$
We can find the maximum acceleration:
$a_m = A~\omega^2$
$a_m = A~(2\pi~f)^2$
$a_m = (1.0\times 10^{-18}~m)~(2\pi)^2~(20.0~Hz)^2$
$a_m = 1.58\times 10^{-14}~m/s^2$
The maximum velocity is $1.26\times 10^{-16}~m/s$
The maximum acceleration is $1.58\times 10^{-14}~m/s^2$
(c) We can find the maximum velocity:
$v_m = A~\omega$
$v_m = A~(2\pi~f)$
$v_m = (1.0\times 10^{-18}~m)~(2\pi)~(20.0\times 10^3~Hz)$
$v_m = 1.26\times 10^{-13}~m/s$
We can find the maximum acceleration:
$a_m = A~\omega^2$
$a_m = A~(2\pi~f)^2$
$a_m = (1.0\times 10^{-18}~m)~(2\pi)^2~(20.0\times 10^3~Hz)^2$
$a_m = 1.58\times 10^{-8}~m/s^2$
The maximum velocity is $1.26\times 10^{-13}~m/s$
The maximum acceleration is $1.58\times 10^{-8}~m/s^2$
