Water waves in a small tank are .06 m long. They pass a given point at a rate of 14.8 waves every three seconds. What is the speed of the water waves? What is the period of these water waves?

Respuesta :

Answer:

Speed = 0.296m/2

Period = 0.203 s

Explanation:

If by 'long' you mean the wavelength of the waves, then the wavelength [tex]\lambda=0.06m[/tex].

The frequency [tex]f[/tex] of the waves is 14.8 waves every 3 seconds or

[tex]f=14.8/3 =4.33Hz[/tex].

Now the relationship between wavelength [tex]\lambda[/tex], frequency [tex]f[/tex] and speed [tex]v[/tex] of the waves is:

[tex]v=\lambda f[/tex]

We put in the values [tex]\lambda=0.06m[/tex] and [tex]f=4.933Hz[/tex] and get:

[tex]\boxed{v=0.06*4.922=0.296m/s}[/tex]

Now the period [tex]T[/tex] is just the inverse of the frequency, or

[tex]T=\frac{1}{f}[/tex]

[tex]\boxed{T=\frac{1}{4.933}=0.203\:seconds }[/tex]

The speed of the wave is 0.2958 m/s and its period is 0.203 second

The speed of a wave is the product of its frequency and wavelength. It is given by:

v = fλ

where f is the frequency, λ is the wavelength and v is the velocity

The frequency (F) = 14.8 waves / 3 seconds = 4.93 wave per second

Speed(v) = Fλ = 4.93 * 0.06 m = 0.2958 m/s

Period (T) = 1/F = 1 / 4.93 = 0.203 second

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