a) The speed of the wave is 234.8 m/s
b) The frequency of the wave is [tex]3.5\cdot 10^{-4} Hz[/tex]
c) The period of the wave is 2849 s
Explanation:
a)
Since the ocean wave travels with a uniform motion, the speed of the wave can be calculated as
[tex]v=\frac{d}{t}[/tex]
where
d is the distance travelled
t is the time elapsed
For the ocean wave in this problem, we have:
[tex]d=3500 km = 3.5\cdot 10^6 m[/tex] is the distance travelled
[tex]t=4.14 h \cdot (60\cdot 60)=14,904 s[/tex] is the time elapsed
Substituting, we find the speed of the wave
[tex]v=\frac{3.5\cdot 10^6}{14904}=234.8 m/s[/tex]
b)
The speed of a wave can also be rewritten by using the wave equation:
[tex]v=f \lambda[/tex]
where
v is the speed
f is the frequency
[tex]\lambda[/tex] is the wavelength of the wave
For the wave in this problem, we have:
v = 234.8 m/s is the speed
[tex]\lambda=669 km = 6.69\cdot 10^5 m[/tex] is the wavelength
Solving for f, we find the frequency:
[tex]f=\frac{v}{\lambda}=\frac{234.8}{6.69\cdot 10^5}=3.5\cdot 10^{-4} Hz[/tex]
c)
The period of a wave is the time the wave takes to do one complete oscillation.
Mathematically, the period is equal to the reciprocal of the frequency:
[tex]T=\frac{1}{f}[/tex]
where
T is the period
f is the frequency
For the ocean wave in this problem, we have
[tex]f=3.5\cdot 10^{-4} Hz[/tex]
Therefore, the period of the wave is
[tex]T=\frac{1}{3.5\cdot 10^{-4}}=2849 s[/tex]
Learn more about speed and frequency of a wave:
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