Answer :
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. [tex]f=\frac{30}{\pi }Hz\\[/tex]
b. [tex]wavelength=\frac{\pi }{3.1}m \\[/tex]
c. [tex]v=9.68m/s[/tex]
Explanation:
The equation of a wave is represented as
[tex]D(x,t)=Asin(kx+wt) \\[/tex]
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
[tex]f=\frac{60}{2\pi }\\f=\frac{30}{\pi }Hz\\[/tex]
b. to determine the wave length, we use
[tex]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 \\[/tex]
c. the wave speed v is express as the product of the frequency and the wavelength. Hence
[tex]v=frequency*wavelength \\v=\frac{30}{\pi } *\frac{\pi }{3.1}\\ v=9.68m/s[/tex]