PHY2606 Assignment 5 2025 Accurate Solutions (685131) Due 18th August 2025

PHY2606
Assignment 5
Unique No: 685131
Due 18th August 2025

, Question 1
A fisherman in a boat on a lake counts crests of a wave passing the boat at a
1
time interval of 2 s between successive crests. Each crest takes 1.5 s to travel
the length of the boat (4.5 m). Determine the frequency, angular frequency,
phase velocity, wavelength, and wavenumber of the water wave.


Solution
Step 1: Determine the frequency

The frequency f is the number of crests passing per unit time. The time
1
interval between successive crests is given as 2 s.

1 1
f= = = 2 Hz.
time interval 0.5

Step 2: Determine the angular frequency

The angular frequency ω is related to the frequency by the equation ω = 2πf .

ω = 2π × 2 = 4π rad/s.

Step 3: Determine the wavelength

The wavelength λ is the distance between successive crests. The time for a
crest to travel the length of the boat (4.5 m) is 1.5 s, and the frequency is 2
distance
Hz. The speed of the wave v can be found using the relationship v = time .

4.5
v= = 3 m/s.
1.5

Since v = f λ, solve for λ:

v 3
λ= = = 1.5 m.
f 2




1