Answer:
a) speed= 0.86m/s
b) Amplitude = 0.35m
C) Amplitude = 0.25m
Explanation: correct values in question (for the boat to travel from its highest point to its lowest, a total distance of 0.700 m . The fisherman sees that the wave crests are spaced 6.00 m apart.)
The speed of a periodic wave with wavelength and frequency is given by:
Speed = frequency × wavelength
The relation between the time period and frequency is given by:
T = 1/f
Given:
Time that the boat takes to travel from the highest point to its lowest point,t = 3.50s
Distance between the lowest point and the highest point,d = 0.70m
Wavelength = 6.0m
a) Wavelength is the distance between two successive wave crests or troughs. So, the distance between the Crest (highest point) to the next(lowest point) is a half wavelength.
The time period ,T is the time between two successive waves.
Therefore,the time it takes the boat to travel from its highest point to its lowest point is period.
T = 2 ×3.50 =7.0seconds
Frequency, f = 1/7.0
f = 0.1429Hz
Speed = frequency × wavelength
Speed = 0.1429 × 6 = 0.86m/s
b) The amplitude is the maximum magnitude of displacement from equilibrium.
Therefore, the distance between the boar's highest point to its lowest point is
Amplitude, A = distance /2
Amplitude A = 0.70/2= 0.35m
c) If the vertical distance changes to d2= 0.50m but other data remained the same, this wont change the speed of the wave because it does not depend on the vertical displacement but it will change the amplitude
A = distance /2 = 0.50m/2 = 0.25m
