Trig type question -- Speed of sound in water and in air

In summary, the problem involves an explosion on the surface of a lake and the distance between the hydrophone and the explosion is unknown. Given the speed of sound in air and water, as well as a delay of 0.3 seconds between the hydrophone and microphone receiving the sound, you can solve for the distance of the hydrophone from the explosion by setting up and solving a linear equation with the time it takes for the microphone and hydrophone to pick up the sound.
  • #1
classicswiss
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Homework Statement
An explosion occurs on the surface of a lake, and the explosion is felt some distance from the site or origin by a hydrophone below the water and by a microphone in air directly above the microphone. Taking the speed of sound in air to be 343m/s and the speed of sound in water to be 1,500 and a delay of 0.3 seconds between both the hydrophone and microphone receiving it, how far is the hydrophone from the explosion?
Relevant Equations
speed= distance / time
unsure
 
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  • #2
classicswiss said:
Homework Statement:: An explosion occurs on the surface of a lake, and the explosion is felt some distance from the site or origin by a hydrophone below the water and by a microphone in air directly above the microphone. Taking the speed of sound in air to be 343m/s and the speed of sound in water to be 1,500 and a delay of 0.3 seconds between both the hydrophone and microphone receiving it, how far is the hydrophone from the explosion?
Relevant Equations:: unsure

unsure
It's a question about distances speeds and times. If you've not encountered any relevant equations for that combo your education is sorely lacking.

Per forum rules , you must show some attempt.
 
  • #3
If we assume that the phrase "directly above the hydrophone" means that the vertical distance between the hydrophone and the microphone is negligible, then it is a simple linear (first degree) equation you have to solve to answer this.
Assume ##x## is the distance of the hydrophone from the explosion and ##t=0 ## is the time that the explosion happens. Try to answer the following two questions (answer will be in terms of ##x## and the speed of sound in water and/or in air)
  1. After how much time ##t_1## the microphone picks the sound ,
  2. After how much time ##t_2## the hydrophone picks the sound.
It is given that ##t_1-t_2=0.3## so if you answer the above two questions, you can plug the expressions of ##t_1## and ##t_2## in the latter equation and solve for ##x##.
 
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Related to Trig type question -- Speed of sound in water and in air

1. What is the speed of sound in water?

The speed of sound in water is approximately 1,500 meters per second, which is about four times faster than the speed of sound in air.

2. How does the speed of sound in water compare to the speed of sound in air?

The speed of sound in water is significantly faster than the speed of sound in air. This is due to the fact that water molecules are more tightly packed together, allowing sound waves to travel more quickly.

3. What factors affect the speed of sound in water?

The speed of sound in water can be affected by several factors, including temperature, salinity, and pressure. As temperature and salinity increase, the speed of sound in water also increases. On the other hand, as pressure increases, the speed of sound in water decreases.

4. How is the speed of sound in water measured?

The speed of sound in water is typically measured using a device called a hydrophone. This device emits a sound wave and then measures the time it takes for the wave to travel through the water and reflect back to the hydrophone. This time can then be used to calculate the speed of sound in water.

5. Why is it important to know the speed of sound in water?

Knowing the speed of sound in water is important for a variety of reasons. It is crucial for underwater communication, navigation, and sonar technology. It also plays a role in understanding the behavior of marine animals and the effects of sound pollution on them.

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