Respuesta :
Answer with Explanation:
We are given that
D(y,t)=[tex]5.20 cm sin (6.40y+63.0t)[/tex]
Where y is in m and t( in sec)
Compare it with general equation of displacement of wave travelling towards left
[tex]y(x,t)=A sin(\omega t+kx)[/tex]
Then, we get A=5.2 cm,[tex]\omega=63[/tex]
[tex]k=6.40 cm[/tex]
a.We now that [tex]\nu=\frac{\omega}{2\pi}[/tex]
Where [tex]\nu[/tex]=Linear frequency
[tex]\omega[/tex]=Angular frequency
[tex]\pi[/tex]=3.14
[tex]\nu=\frac{63}{2\cdot 3.14}=10Hz[/tex]
b.[tex]k=\frac{2pi}{\lambda}[/tex]
[tex]\lambda=\frac{2\pi}{k}[/tex]
Substitute the values then we get
[tex]\lambda=\frac{2\times 3.14}{6.4}[/tex]
[tex]\lambda=0.98 cm[/tex]
Hence, the wavelength of the wave=0.98 cm
c.[tex]v=\nu\times \lambda[/tex]
Substitute the values then we get
[tex]v=10\times 0.98=9.8 cm/s[/tex]
Hence, the speed of the wave=9.8 cm/s
a. The frequency of the wave is [tex]10 Hz[/tex]
b. The wavelength of the wave is [tex]0.98m[/tex]
c. The speed of the wave is [tex]9.8m/s[/tex]
Equation of Wave:
The equation of the wave is,
[tex]D(y,t)=Asin(wt+ky)[/tex]
where,
- D is the displacement
- A is amplitude
- ω is the angular frequency
- T is the time period ,
- k is a constant which is equal to 2πλ , where λ is the wavelength
The Displacement of wave is given by,
[tex]D(y,t)=5.2sin(63t+6.4y)[/tex]
Compare above function from, [tex]D(y,t)=Asin(wt+ky)[/tex]
We get,[tex]A=5.2, w=63,k=6.4[/tex]
Linear frequency, [tex]\nu=\frac{w}{2\pi}=\frac{63}{2*3.14}=10Hz[/tex]
The wavelength of this wave is,
[tex]\lambda=\frac{2\pi}{k} =\frac{2*3.14}{6.4} =0.98m[/tex]
The speed of this wave is, [tex]v=\nu*\lambda=10*0.98=9.8m/s[/tex]
Find out more information about the Wavelength of wave here:
https://brainly.com/question/10728818
