Calculate distance from expolision - Waves

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In summary, a recording station observed a 68-second interval between the reception of P and S waves from an underground nuclear test explosion, with speeds of 7800 ms^-1 and 4200 ms^-1 respectively. Using the equation for motion with constant speed, the distance of the test site from the explosion can be calculated by taking the difference in propagation times (68 seconds) and multiplying it by the respective speeds of the waves. The resulting distance is 620 km.
  • #1
Jason17
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Homework Statement


A recording station observed that there was an interval of 68s between the reception of P (push or primary) waves and S (shake or secondary waves) from an underground nuclear test explosion.
The speed of P and S waves in the Earths crust are 7800 ms^-1 and 4200 ms^-1, respectively.

Calculate the distance of the test site from the explosion


Homework Equations


Speed = Frequency x wavelength (v=fλ)
Speed of electromagnetic radiation = 3 x 10^8 ms^-1
Speed of sound in air 340 ms^-1
Speed of sound in water and sea water = 1500 ms^-1

The Attempt at a Solution


So I am using this formula:
Speed = Frequency x wavelength (v=fλ)
I have the speed, 7800 & 4200 and its frequency i believe? is 68 seconds

Im trying to find the distance (is this the wavelength?)
Wavelength= Speed/Frequency

The answer is 620 km. Which i cannot get to :\

Help appreciated, ty in advance
 
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  • #2


You don't really need any of the formulas that you wrote.
You know the speed already.
68s is not frequency but the time difference between the detection of the two waves.

Just use the equation for motion with constant speed for each one of the waves.
 
  • #3


sorry, i don't understand what your trying to say.

Equation of motion?
S=u.t + 0.5.a.t^2 ?
or
S=(u+v)/2 . t?

I still can't get to 620km :(
 
  • #4


No, the wave has constant speed.
So it's just
d=u1*t1
and
d=u2*t2

where d is the distance between source and receptor and t1, t2 are the propagation times for the two waves.
You don't know t1 and t2 but you know the difference, t1-t2=68 s.
Can you solve the problem now? You need to find d.
 

1. How do you calculate the distance from an explosion using waves?

To calculate the distance from an explosion, you can use the formula d = (v x t)/2, where d is the distance, v is the velocity of the wave, and t is the time it takes for the wave to reach the observer. This formula works for both sound waves and shock waves.

2. What is the difference between sound waves and shock waves?

Sound waves are longitudinal waves that require a medium (such as air or water) to travel through, while shock waves are transverse waves that can travel through any medium. Shock waves are also characterized by a sudden and drastic increase in pressure, often caused by an explosion or supersonic motion.

3. Can you calculate the distance from an explosion using only one type of wave?

Yes, you can calculate the distance from an explosion using either sound waves or shock waves. However, using both types of waves can provide a more accurate result as shock waves may dissipate faster than sound waves.

4. How does the intensity of the explosion affect the distance calculation using waves?

The intensity of an explosion can affect the distance calculation using waves as it can impact the velocity of the waves. A more intense explosion may produce stronger and faster waves, which can reach the observer in a shorter amount of time, resulting in a shorter distance calculation.

5. Are there any other factors that can affect the accuracy of distance calculations using waves?

Yes, there are several other factors that can affect the accuracy of distance calculations using waves. These include atmospheric conditions, such as wind or temperature, which can alter the velocity of the waves. Obstacles in the wave's path, such as buildings or mountains, can also cause the wave to travel a longer distance before reaching the observer.

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