Respuesta :
Answer:
n = 7.5 times/minute
Explanation:
Given that,
Wavelength of the ocean wave, [tex]\lambda=40\ m[/tex]
The speed of the ocean wave, v = 5 m/s
To find,
Number of times a minute does a boat bob up and down on ocean waves.
Solution,
The relation between the speed of wave, wavelength and frequency is given by :
[tex]v=f\times \lambda[/tex]
[tex]f=\dfrac{v}{\lambda}[/tex]
[tex]f=\dfrac{5\ m/s}{40\ m}[/tex]
f = 0.125 Hz
The number of times per minute the bob moves up and down is given by :
[tex]n=f\times t[/tex]
[tex]n=0.125\times 60[/tex]
n = 7.5 times/minute
So, its will move up and down in 7.5 times/minute. Therefore, this is the required solution.
Taking into account the definition of wavelength, frecuency and propagation speed, the number of times per minute the bob moves up and down is 7.5 times per minute.
Wavelength
Wavelength is the minimum distance between two successive points on the wave that are in the same state of vibration. It is expressed in units of length (m).
Frequency
Frequency is the number of vibrations that occur in a unit of time. Its unit is s⁻¹ or hertz (Hz).
Propagation speed
Finally, the propagation speed is the speed with which the wave propagates in the medium, that is, it is the magnitude that measures the speed at which the wave disturbance propagates along its displacement.
The propagation speed relate the wavelength (λ) and the frequency (f) inversely proportional using the following equation:
v = f× λ
Amount of times in a minute that a boat bob up and down on ocean waves
In this case, you know:
- v= 5 [tex]\frac{m}{s^{2} }[/tex]
- f= ?
- λ= 40 m
Replacing in the definition of propagation speed:
5 [tex]\frac{m}{s^{2} }[/tex]= f× 40 m
Solving:
f= 5 [tex]\frac{m}{s^{2} }[/tex]÷ 40 m
f= 0.125 Hz= 0.125 [tex]\frac{1}{seconds}[/tex]
Then, a boat bob up and down on ocean waves 0.125 times in a second.
So, the number of times per minute the bob moves up and down is given by:
n= f× time
n= 0.125 Hz× 60 minutes in 1 second
n=7.5 times per minute
Finally, the number of times per minute the bob moves up and down is 7.5 times per minute.
Learn more about wavelength, frecuency and propagation speed:
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