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]](https://tex.z-dn.net/?f=y%28x%2Ct%29%3DA%5Ccos%5Cleft%5B2%5Cpi%5Cleft%28%20%5Cfrac%7Bx%7D%7B%5Clambda%7D%20-%20%5Cfrac%7Bt%7D%7BT%7D%20%5Cright%29%5Cright%5D)
,
where A is the amplitude,
![\lambda](https://tex.z-dn.net/?f=%5Clambda)
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)]](https://tex.z-dn.net/?f=y%28x%2Ct%29%3Dbcos%5B2%5Cpi%28xl-t%5Ctau%29%5D)
, where <span>b = 5.90 mm , l = 28.0 cm , and
![\tau = 3.40\times10^{-2} s](https://tex.z-dn.net/?f=%5Ctau%20%3D%203.40%5Ctimes10%5E%7B-2%7D%20s)
.
Thus, the amplitude is b = 5.90 mm =
![5.9\times10^{-3} \ m](https://tex.z-dn.net/?f=5.9%5Ctimes10%5E%7B-3%7D%20%5C%20m)
.
Part B:
</span>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]](https://tex.z-dn.net/?f=y%28x%2Ct%29%3DA%5Ccos%5Cleft%5B2%5Cpi%5Cleft%28%20%5Cfrac%7Bx%7D%7B%5Clambda%7D%20-%20%5Cfrac%7Bt%7D%7BT%7D%20%5Cright%29%5Cright%5D)
,
where A is the amplitude,
![\lambda](https://tex.z-dn.net/?f=%5Clambda)
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]](https://tex.z-dn.net/?f=y%28x%2Ct%29%3Dbcos%5B2%5Cpi%5Cleft%28%5Cfrac%7Bx%7D%7Bl%7D-%5Cfrac%7Bt%7D%7Btau%7D%5Cright%29%5Cright%5D)
, where <span>b = 5.90 mm , l = 28.0 cm , and
![\tau = 3.40\times10^{-2} s](https://tex.z-dn.net/?f=%5Ctau%20%3D%203.40%5Ctimes10%5E%7B-2%7D%20s)
.
Thus,
</span><span>
![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}}](https://tex.z-dn.net/?f=y%28x%2Ct%29%3Dbcos%5B2%5Cpi%5Cleft%28%5Cfrac%7Bx%7D%7Bl%7D-%5Cfrac%7Bt%7D%7Btau%7D%5Cright%29%5Cright%5Btex%5D%20%0A%5Cfrac%7B1%7D%7B%5Clambda%7D%20%3D%20%5Cfrac%7B1%7D%7Bl%7D%20%20%5C%5C%20%20%5C%5C%20%20%5CRightarrow%5Clambda%3D%20l%20%3D28.0%20%5C%20%0Acm%3D%5Cbold%7B2.8%5Ctimes10%5E%7B-1%7D%7D%20)
Therefore, the wavelength is 28.0 cm =
![2.8\times10^{-1} \ m](https://tex.z-dn.net/?f=2.8%5Ctimes10%5E%7B-1%7D%20%5C%20m)
.
Part C:
</span>
<span>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]](https://tex.z-dn.net/?f=y%28x%2Ct%29%3DA%5Ccos%5Cleft%5B2%5Cpi%5Cleft%28%20%5Cfrac%7Bx%7D%7B%5Clambda%7D%20-%20%5Cfrac%7Bt%7D%7BT%7D%20%5Cright%29%5Cright%5D)
,
where A is the amplitude,
![\lambda](https://tex.z-dn.net/?f=%5Clambda)
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]](https://tex.z-dn.net/?f=y%28x%2Ct%29%3Dbcos%5B2%5Cpi%5Cleft%28%5Cfrac%7Bx%7D%7Bl%7D-%5Cfrac%7Bt%7D%7Btau%7D%5Cright%29%5Cright%5D)
,
where <span>b = 5.90 mm , l = 28.0 cm , and
![\tau = 3.40\times10^{-2} s](https://tex.z-dn.net/?f=%5Ctau%20%3D%203.40%5Ctimes10%5E%7B-2%7D%20s)
.
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}](https://tex.z-dn.net/?f=f%3D%20%5Cfrac%7B1%7D%7BT%7D%20%3D%20%5Cfrac%7B1%7D%7B%5Ctau%7D%20%3D%20%5Cfrac%7B1%7D%7B3.40%5Ctimes10%5E%7B-2%7D%7D%20%3D%5Cbold%7B29.4%20%5C%20Hz%7D)
</span><span>
Part D:
</span></span>
Given that the <span><span><span>the wavelength is
![2.8\times10^{-1} \ m](https://tex.z-dn.net/?f=2.8%5Ctimes10%5E%7B-1%7D%20%5C%20m)
</span> and that the wave's frequency is 29.4 Hz</span></span>
The wave's speed of propagation, v, is given by: