Question

EXAMPLE 14.1 Explosion over an Ice Sheet Goal Calculate time of travel for sound through various media. Problem An explosion occurs 275 m above an 867-m-thick ice sheet that lies over ocean water. If the air temperature is -7.00°C, how long does i take the sound to reach a research vessel 1 250 m below the ice? Neglect any changes in the bulk modulus and density with temperature and depth. (Use Bice-9.2 >< 109 Pa) Strategy Calculate the speed of sound in air with Equation 14.4 and use d-t to find the time needed for the sound to reach the surface of the ice. Use Equation 14.1 to compute the speed of sound in ice, again finding the time with the distance equation. Finally, use the speed of sound in salt water to find the time needed to traverse the water and then sum the three times. Solution Calculate the speed of sound in air at-7.00℃, which is equivalent to 266 K: V273 K (331 m/s) 266 K V 2731-= 327 m/s 275 m rair 327 m/s 0.841 s Calculate the travel time through the air: 9.2 109 Pa p V 917 kg/m = 3.2 × 103 m/s Compute the speed of sound in ice, using the bullk modulus and density of ice: 867 m Compute the travel time through the ice: 0.27 s ceVice3 200 m/s 1 250 m Compute the travel time through the ocean water: 530 m/S Sum the three times to obtain the total time of propagation: tot air + lice+Iw0.841 s 0.27s+0.817 s

How did they get the density of ice and velocity of water here? Plz, tell me how to get these value by calculation.

Thanks

Answer 1

See that both of these values are constant values, these cannot be calculated by a equation, we need to do experiments to calculate exact value of these. THERE IS NO METHOD TO CALCULATE THEM.

density of ice = 917 kg/m^3

If you want to do experiment then

take a cube of ice out of refrigerator, now measure it's dimensions by a scale.

Density = mass/Volume

Calculate the exact mass of cube using weighing scale

Calculate volume = length*height*width

Now divide both values you will get the value of density around 917 kg/m^3

Now take different size of cubes and repeat this experiment you will always get the value around 917 kg/m^3

Similarly there are various experiments to calculate the speed of sound in water, but the final velocity will always be around 1530 m/sec. There can be some experimental error.

So you have to remember these values and use them in calculation whenever required.

Also why did you only ask about these two values, and not about the value of speed of sound in ice = 3200 m/sec, and value of Bulk modulus of ice = 9.2*10^9 Pa etc. these values are also constant and we use them directly whenever required.

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