Jie Yu completed a physics learning objective to calculate how long it takes for the sound from a ship to diminish to 60dB. The ship was moving away from the observer at 40 m/s and was initially 2km away. Using the sound intensity level equation and treating the ship as an isotropic source, the calculation found the distance at which the sound intensity equals 10-6 W/m2. Subtracting the initial distance and dividing by the velocity then provided the time of 49.7 seconds.

1. Name: Jie Yu
Student Number: 23362130
Session: L2J
PHYS 101 Learning Objectives
You are standing on the riverbank and are 2km meters apart from a ship that is
moving away from you at a constant velocity of 40 m/s. The ship radiates sound
with power of 200W. Assume isotropic source.
How long does it takes for the sound to diminish to 60dB at your position if you are
stationary?
Explanation
Using the sound intensity level equation we could find that the sound intensity of
the ship you receive. Its assumed isotropic source, we could calculate the distance
the ship between you and the ship with known power (P) and sound intensity
(𝐼𝑠ℎ𝑖𝑝 ). After that, we could find the distance traveled during this period of time and
therefore calculate the time with know distance and velocity.
Answers
β(I) = 0dB + 10log(
𝐼 𝑠ℎ𝑖𝑝
𝐼0
) =60dB
log(
𝐼𝑠ℎ𝑖𝑝
𝐼0
) = 6dB
𝐼𝑠ℎ𝑖𝑝 =𝐼0×106
= 10−6
W
I=
𝑃
4𝜋𝑟2
r = √
𝑃
𝐼4𝜋
=√
200𝑊
(10−6 𝑊/𝑚2 )(4𝜋)
= 3989.4m
Distance the ship traveled: 3989.4m – 2000m = 1989.4
t =
𝑑
𝑣
=
1989.4𝑚
40𝑚 /𝑠
= 49.7s