Question

A fisherman notices that his boat is moving up and down periodically, owing to waves on the surface of the water. It takes a time of 2.70 s 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 a horizontal distance of 6.50 m apart. a. How fast are the waves traveling? b. What is the amplitude A of each wave?

Answer 1

Answer: a. 1.203 m/s   b.0.35m

Explanation:

a. Velocity of the waves

The velocity $V$ of a wave is given by the following equation:

$V=\frac{\lambda}{T}$  (1)

Where:

$\lambda=6.50m$ is the wavelength (the horizontal space between crest and crest)

$T=2.70s.2=5.4s$ is the period of the wave (If we were told it takes a time of 2.70 s for the boat to travel from its highest point to its lowest, the period is twice this amount, which is the time it takes to travel one wavelength)

Substituting the known values:

$V=\frac{6.50m}{5.4s}=1.203m/s$  (2)

$V=1.203m/s$  Velocity of the wave

b. Amplitude of each wave

The amplitude $A$ of a wave is defined is given by the following equation:

$A=\frac{maximumpoint-minimumpoint}{2}$  (3)

If we know the total distance between the highest point to the lowest point is 0.7 m. This means:

$maximumpoint-minimumpoint=0.7m$

Substituting this value in (3):

$A=\frac{0.7m}{2}$  (4)

$A=0.35m$  This is the amplitude of the wave

Answer 2

The waves for the boat of fisherman is travelling with the speed of 1.203 m/s and the amplitude of each wave is 0.35 m.

What is speed of wave?

Speed of wave is the rate of speed by which the wave travel the distance in the time taken by it.

The distance traveled by the boat  from its highest point to the lowest point is 0.700 m. The time taken by the boat is 2.70.

The fisherman sees that the wave crests are spaced a horizontal distance of 6.50 m apart. As, the horizontal distance of crests is the wavelength of the wave. Thus, the wavelength of the wave is,

$\lambda=6.50\rm s$

The period of the wave is twice the time taken from highest to lowest point. Thus, the time period of the wave is,

$T=2\times2.7\\T=5.4\rm s$

The speed of the wave is the ratio of wavelength to the time period. Thus, the speed of the waves travelling is,

$v=\dfrac{6.50}{5.4}\\v=1.203\rm m/s$

The amplitude of wave is the half of the difference of highest point to the lowest point of the wave.

Now, the distance traveled by the boat  from its highest point to the lowest point is 0.700 m. Thus, the amplitude of each wave is,

$A=\dfrac{0.7}{2}A=0.35\rm m$

Thus, the waves for the boat of fisherman is travelling with the speed of 1.203 m/s and the amplitude of each wave is 0.35 m.

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