Question

9. A wave on Beaver Dam Lake passes by two docks that are 40.0 m apart.
a. If there is a crest at each dock and another three crests between the two docks, determine the
wavelength.
b. If 10 waves pass one dock every 16.0 seconds, determine the period and frequency of the wave.
.

c. What is the speed of the wave?

Answer 1

Answers:

a) 10 m

b) time=1.6 s, frquency=0.625 Hz

c) 6.25 m/s

Explanation:

a) If there is a crest at each dock and another three crests between the two docks, and the wavelength $\lambda$ is the distance between to crests; this means we have $4\lambda$ in $40 m$:

$40 m=4\lambda$

Clearing $\lambda$:

$\lambda=\frac{40 m}{4}$

$\lambda=10 m$

b) This part can be solved by a Rule of Three:

If 10 waves ---- 16 s

1 wave ----- $T$

Then:

$T=\frac{(1 wave)(16 s)}{10 waves}$

$T=1.6 s$ This is the period of the wave

On the other hand, the frequency $f$ of the wave has an inverse relation with its period $T$:

$f=\frac{1}{T}$

$f=\frac{1}{1.6 s}$

$f=0.625 Hz$ This is the frequency of the wave

c) The speed $v$ of a wave is given by the following equation:

$v=\frac{\lambda}{T}$

$v=\frac{10 m}{1.6 s}$

Finally:

$v=6.25 m/s$