fertilizeki

2022-01-12

While anchored in the middle of a lake, you count exactly three waves hitting your boat every 10 s. You raise anchor and start motoring slowly in the same direction the waves are going. When traveling at 1.5 m/s, you notice that exactly two waves are hitting the boat from behind every 10 s. What is the speed of the waves on the lake?

Melissa Moore

Beginner2022-01-13Added 32 answers

Step 1

Solve for$f}_{s$ :

${f}_{s}=\frac{3.0}{10}s=0.30Hz$

When you are moving, the measured frequency is expressed as:

${f}_{-}=\frac{2.0}{10}s=0.20Hz$

By application of the equation$f}_{-}=\left(1\frac{{v}_{s}}{v}\right){f}_{s$ , we have:

$\frac{{f}_{-}}{{f}_{+}}=1-\frac{{v}_{s}}{v}$

$\frac{{v}_{s}}{v}=1-\frac{{f}_{-}}{{f}_{s}}$

$v={v}_{s}\left(\frac{1}{1-\frac{{f}_{-}}{{f}_{s}}}\right)$

$v={v}_{s}\left(\frac{{f}_{s}}{{f}_{s}-{f}_{-}}\right)$

$v=\left(1.5\frac{m}{s}\right)\left(\frac{0.30Hz}{0.30Hz-0.20Hz}\right)=4.5\frac{m}{s}$

Solve for

When you are moving, the measured frequency is expressed as:

By application of the equation