## College Physics (4th Edition)

(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 $1.58\times 10^{-8}~m/s^2$
(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 $1.58\times 10^{-8}~m/s^2$