Question

A fisherman notices that his boat is moving up and down periodically, owing to waves on the surface of the water. It takes 3.50 ss for the boat to travel from its highest point to its lowest, a total distance of 0.700 mm . The fisherman sees that the wave crests are spaced 6.00 mm apart.
How fast are the waves traveling? in m/s

What is the amplitude of each wave? in m

If the total vertical distance traveled by the boat were 0.500 , but the other data remained the same, how fast are the waves traveling ? in m/s

If the total vertical distance traveled by the boat were 0.500 , but the other data remained the same, what is the amplitude of each wave? in m

Answer 1

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

Answer 2

The correct values from the question are;

a total distance of 0.7m and wave crests are spaced 6.00 m apart

Answer:

A) Speed = 0.8574 m/s

B) A = 0.35m

C) Velocity remains unchanged as 0.8574m/s and while A = 0.25m

Explanation:

A) We know that wavelength λ is the distance between two successive wave crests or troughs, so the wavelength here is 6m.

From the question, it takes 3.5 seconds to travel from its highest point to its lowest point which is half period. Thus, full period T is;

T = 2 x 3.5 = 7 seconds

Now, we know that frequency is given as;

f = 1/T.

Thus, f = 1/7 = 0.1429 Hz

We know that speed of wave is given by;

V = fλ

Thus V= 0.1429 x 6 = 0.8574 m/s

B) Amplitude(A) is the maximum magnitude of displacement from equilibrium. This implies that the distance between the boat's highest point to its lowest point is 2A. From the question, d = 0.7m

Thus, 2A = d = 0.7

Thus,A = 0.7/2 = 0.35m

C) Since the vertical distance is now 0.5m and the other values remain the same. Thus, the speed will remain the same because it doesn't depend on vertical displacement.

Thus, v remains 0.8574 m/s.

Amplitude will now be calculated;

A = 0.5/2 = 0.25m