Mathematics: Acertain transverse wave is described by y(x,t)=bcos[2π(xl−tτ)], where b = 5.90 mm , l = 28.0 cm , and τ = 3.40×10−2 s .

X-3y=18-x -x-3y= -x+18Divide -3 from both sides Y=1/3x-6...

Acertain transverse wave is described by y(x,t)=bcos[2π(xl−tτ)],

Ответ:

naleyah

13.03.2022

Part A:

The general form of the equation of a transverse wave is given by:

$y(x,t)=A\cos\left[2\pi\left( \frac{x}{\lambda} - \frac{t}{T} \right)\right]$ ,

where A is the amplitude, $\lambda$ is the wavelength, and T is the period.

Given that a certain transverse wave is described by $y(x,t)=bcos[2\pi(xl-t\tau)]$ , where b = 5.90 mm , l = 28.0 cm , and $\tau = 3.40\times10^{-2} s$ .

Thus, the amplitude is b = 5.90 mm = $5.9\times10^{-3} \ m$ .

Part B:

The general form of the equation of a transverse wave is given by:

$y(x,t)=A\cos\left[2\pi\left( \frac{x}{\lambda} - \frac{t}{T} \right)\right]$ ,

where A is the amplitude, $\lambda$ is the wavelength, and T is the period.

Given that a certain transverse wave is described by $y(x,t)=bcos[2\pi\left(\frac{x}{l}-\frac{t}{tau}\right)\right]$ , where b = 5.90 mm , l = 28.0 cm , and $\tau = 3.40\times10^{-2} s$ .

Thus,

$y(x,t)=bcos[2\pi\left(\frac{x}{l}-\frac{t}{tau}\right)\right[tex] 
\frac{1}{\lambda} = \frac{1}{l} \\ \\ \Rightarrow\lambda= l =28.0 \ 
cm=\bold{2.8\times10^{-1}}$

Therefore, the wavelength is 28.0 cm = $2.8\times10^{-1} \ m$ .

Part C:

The general form of the equation of a transverse wave is given by:

$y(x,t)=A\cos\left[2\pi\left( \frac{x}{\lambda} - \frac{t}{T} \right)\right]$ ,

where A is the amplitude, $\lambda$ is the wavelength, and T is the period.

Given that a certain transverse wave is described by $y(x,t)=bcos[2\pi\left(\frac{x}{l}-\frac{t}{tau}\right)\right]$ , where b = 5.90 mm , l = 28.0 cm , and $\tau = 3.40\times10^{-2} s$ .

The wave's frequency, f, is given by:

$f= \frac{1}{T} = \frac{1}{\tau} = \frac{1}{3.40\times10^{-2}} =\bold{29.4 \ Hz}$

Part D:

Given that the the wavelength is $2.8\times10^{-1} \ m$ and that the wave's frequency is 29.4 Hz

The wave's speed of propagation, v, is given by:

$v=f\lambda=29.4(2.8\times10^{-1})=8.232 \ m/s$

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Acertain transverse wave is described by y(x,t)=bcos[2π(xl−tτ)], where b = 5.90 mm , l = 28.0 cm , and τ = 3.40×10−2 s .

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