Question

You are still at the grand canyon, and you see a little kid throw his tickle me Elmo doll over the railing! You can hear Elmo laughing as he plummets toward the canyon floor hundreds of feet below. Elmos laugh is usually a 5000 Hz sound, but you can hear the Elmos laugh was only a 4300 Hz sound just before Elmo hit the ground. How fast was Elmo falling?

Answer 1

We will use the equation of doppler effects

`\begin{gathered} f=(v+vo)/(v+vs)f0 \\ (f)/(fo)=(v+vo)/(v+vs) \\ (f)/(fo(v+vo))=(1)/(v+vs) \\ vs=(fo(v+vo))/(f)-v \end{gathered}`

f=5000Hz

f0=4300 Hz

v0=0

v=1238 km/h speed of the sound on the air

`vs=(5000(1238+0))/(4300)-1238`
`vs=201.53\text{ km/h}`
`vs=55.98\text{ m/s}=56\text{ m/s}`