Answer:
The question is incomplete, below is the complete question
"The displacement of a wave traveling in the negative y-direction is D(y,t) = ( 4.60cm ) sin ( 6.20 y+ 60.0 t ), where y is in m and t is in s.
A) What is the frequency of this wave?
B) What is the wavelength of this wave?
C) What is the speed of this wave?"
Answers:
a. ![f=\frac{30}{\pi }Hz\\](https://tex.z-dn.net/?f=f%3D%5Cfrac%7B30%7D%7B%5Cpi%20%7DHz%5C%5C)
b. ![wavelength=\frac{\pi }{3.1}m \\](https://tex.z-dn.net/?f=wavelength%3D%5Cfrac%7B%5Cpi%20%7D%7B3.1%7Dm%20%5C%5C)
c. ![v=9.68m/s](https://tex.z-dn.net/?f=v%3D9.68m%2Fs)
Explanation:
The equation of a wave is represented as
![D(x,t)=Asin(kx+wt) \\](https://tex.z-dn.net/?f=D%28x%2Ct%29%3DAsin%28kx%2Bwt%29%20%5C%5C)
Where A=amplitude
w=angular frequency=2πf
K=wave numbers =2π/λ
since we re giving he equation D(y,t) = ( 4.60cm ) sin ( 6.20 y+ 60.0 t ),
we can compare and get the value for the wave number and angular frequency.
By comparing we have
w=60rads/s
k=6.20
a. to determine the frequency, from the expression fr angular wave frequency we have
w=2πf hence
f=w/2π
if we substitute we arrive at
![f=\frac{60}{2\pi }\\f=\frac{30}{\pi }Hz\\](https://tex.z-dn.net/?f=f%3D%5Cfrac%7B60%7D%7B2%5Cpi%20%7D%5C%5Cf%3D%5Cfrac%7B30%7D%7B%5Cpi%20%7DHz%5C%5C)
b. to determine the wave length, we use
![k=\frac{2\pi }{wavelength} \\k=6.2\\wavelength=\frac{2\pi }{k} \\wavelength=\frac{2\pi }{6.2} \\wavelength=\frac{\pi }{3.1}m \\](https://tex.z-dn.net/?f=k%3D%5Cfrac%7B2%5Cpi%20%7D%7Bwavelength%7D%20%5C%5Ck%3D6.2%5C%5Cwavelength%3D%5Cfrac%7B2%5Cpi%20%7D%7Bk%7D%20%5C%5Cwavelength%3D%5Cfrac%7B2%5Cpi%20%7D%7B6.2%7D%20%5C%5Cwavelength%3D%5Cfrac%7B%5Cpi%20%7D%7B3.1%7Dm%20%5C%5C)
c. the wave speed v is express as the product of the frequency and the wavelength. Hence
![v=frequency*wavelength \\v=\frac{30}{\pi } *\frac{\pi }{3.1}\\ v=9.68m/s](https://tex.z-dn.net/?f=v%3Dfrequency%2Awavelength%20%5C%5Cv%3D%5Cfrac%7B30%7D%7B%5Cpi%20%7D%20%2A%5Cfrac%7B%5Cpi%20%7D%7B3.1%7D%5C%5C%20v%3D9.68m%2Fs)