Question

The frequency F of a fire truck siren heard by a stationary observer is given below, where ± v represents the velocity of the accelerating fire truck in meters per second (see figure). (Round your answers to 3 decimal places).

Answer 1

In order to calculate the rate of change, we can use the following derivatives:

`\begin{gathered} u=(1)/(a+x) \\ (du)/(dx)=-(1)/((a+x)^2) \\ \\ u=(1)/(a-x) \\ (du)/(dx)=(1)/((a-x)^2) \end{gathered}`

So, calculating the rate of change in each case, we have:

a)

`\begin{gathered} F=(130600)/(321-x) \\ (dF)/(dx)=(130600)/((321-x)^2)=(130600)/((321-25)^2)=(130600)/(296^2)=(130600)/(87616)=1.491 \end{gathered}`

b)

`\begin{gathered} F=(130600)/(321+x) \\ (dF)/(dx)=-(130600)/((321+x)^2)=-(130600)/((321+25)^2)=-(130600)/(346^2)=-(130600)/(119716)=-1.091 \end{gathered}`