As ocean waves approach shore, their velocity decreases. How does a decrease in velocity affect the frequency and wavelength of
2 answers:
Explanation:
As ocean waves approach shore, their velocity decreases. The relation between the velocity, wavelength and the frequency of a wave is given by :
f = frequency
= wavelength
..............(1)
So, as the velocity of the wave increases, the wavelength and frequency also increases as per equation (1). When the velocity decreases, the frequency and the wavelength also decreases.
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Answer:
(1) 120°
Explanation:
The wheel is purely rolling, which means it rotates about an axis through the point where it touches the ground (see Figure 11-6).
The net velocity at point P on the periphery, relative to the bottom of the wheel, is:
v = ωr
where r is the distance from the point at the bottom of the wheel to P (see diagram).
To find r, we need to use some geometry. From Inscribed Angle Theorem, we know the inscribed angle is half the arc angle. And from Thales' Theorem, we know an angle inscribed across a diameter is a right angle.
Therefore:
cos (θ/2) = r / (2R)
r = 2R cos (θ/2)
So the net velocity at P is:
v = 2Rω cos (θ/2)
We want this to equal the velocity at the center of the circle, which is Rω.
Rω = 2Rω cos (θ/2)
1 = 2 cos (θ/2)
cos (θ/2) = 1/2
θ/2 = 60°
θ = 120°
