PHYS 101 project

1. PHYS 101 Learning Object:
Sound Waves Explanation Question
Question:Suppose a veryloud sound (easilyheardfrom hundredsof metersaway) isproduced right at the surface of
the water, 100 metersfrom the shore. Whowouldhear the sound first,a personstanding on the shore,or a diver100
metersbelowthe point where the sound was produced? Explainyour solutionstrategy.
For reference:Bair = 1.01 * 105
Pa, Bwater = 2.2 * 109
Pa

2. PHYS 101 Learning Object:
Sound Waves Explanation Question (Solution)
Explanation:
To help solve thisquestion,it is helpful todraw a diagram ofthe describedsituation:
From this diagram, we see that the sound impulse will travel 100 m in a straight line towards the shore, and 100 m in
a straight line towards the diver.From first glance,it seemsthat the sound will reach both points at the same time
because the distance is equal,but will it?
The sound impulse will have to travel through air horizontallyand through water verticallydown. Because the
physical propertiesof these two mediumsare significantlydifferent,their bulkmoduli (ratiosofchangein pressure
over the fractional changeinvolume) are different.
Bair = 1.01 * 105
Pa, Bwater = 2.2 * 109
Pa
Due to this difference,the speedofthe sound wave will be differentinthe two cases. Therefore we needto
determine these speeds,andcomparing themwe will be able to answer the question.
Similarto the speedof a wave on a string, 𝒗 = √
𝑻
𝝁
, the speedofsound through a mediumcan be expressedas
𝒗 = √
𝐁
𝝆
.
We know the densitiesofair and water under normal conditionsare:
Ρair = 1.2 kg/m3 , Ρwater = 1000 kg/m3
Therefore:
Vair = √
𝟏.𝟎𝟏 ∗ 𝟏𝟎 𝟓
𝟏.𝟐
= 290.11 m/s. Tair =
𝟏𝟎𝟎 𝒎
𝟐𝟗𝟎.𝟏𝟏 𝒎/𝒔
= 0.345 s.
Vwater = √
𝟐.𝟐 ∗ 𝟏𝟎 𝟗
𝟏𝟎𝟎𝟎
= 1483.24 m/s Twater =
𝟏𝟎𝟎 𝒎
𝟏𝟒𝟖𝟑.𝟐𝟒 𝒎/𝒔
= 0.067 s.
The diver will hear the sound first.
Soundsource
shore
diver