A boat sounds a fog horn on a day when both the sea water and the air temperature are 25.0 $\degree$ C.The speed of sound in sea water is 1 533 m/s.How much earlier (in s)does a dolphin 1 000 m from the source hear the sound than a person in a boat that is also 1 000 m distant? (Ignore the time it takes the sound to reach the water surface. )
A)0.652
B)2.12
C)2.24
D)2.77
E)2.90

Question

Quizplus · Accepted Answer

We can use the formula for the speed of sound in air at a given temperature:

v_air = 331.3 + 0.61T

where T is the temperature in Celsius. At 25.0°C, we get:

v_air = 331.3 + 0.61(25.0) = 343.8 m/s

Next, we can calculate the time it takes for the sound to travel 1000 meters in air and sea water:

t_air = d/v_air = 1000/343.8 = 2.91 s
t_water = d/v_water = 1000/1533 = 0.652 s

Therefore, the dolphin hears the sound 2.91 - 0.652 = 2.24 seconds earlier than the person in the boat. The answer is (C).

A Boat Sounds a Fog Horn on a Day When °\degree°

A Boat Sounds a Fog Horn on a Day When $\degree$