A large volcanic eruption triggers a tsunami. At a seismic station 250 km away,

Question

A large volcanic eruption triggers a tsunami. At a seismic station 250 km away, the instruments record that the time difference between the arrival of the tidal wave and the arrival of the sound of the explosion is 9.25 min. Tsunamis typically travel at approximately 800 km/h. (Use 343 m/s for the speed of sound in air. Use 2.00 109 Pa and 1000 kg/m3 as the bulk modulus of water and the density of water, respectively.) (a) Which sound arrives first, the sound in the air or in the water? a.)The sound in the air arrives first. b.)The sound in the water arrives first.

Prove your answer numerically. vsound, air = m/s ; vsound, water = m/s

(b) How long after the explosion does it take for the first sound wave to reach the seismic station? min

(c) How long after the explosion does it take for the tsunami to reach the seismic station? min

Explanation / Answer

a. Speed of sound in air=343m/s

To calculate the speed of sound in water v=square root(bulk modulus of water/density of water)

Bulk modulus of water=2*109Pa

Density of water=1000kg/m3

=square root(2*109 /1000)

=square root(2*10-3*109)

=square root(2*106)

=1414.2m/s

Since speed of sound in water is 1414.2m/s and speed of sound in air is 343m/s. Therefore sound in air travels faster than than in the water, so it will appear first.

b. Speed of sound in air=343m/s=20.58km/min

distance from seismic station= 250km

Therefore time taken=distance/speed

=250km/20.58km/min

=12.14 minutes

c. Speed of tsunami wave=800km/hr=13.33km/min

Distance=250km

Time taken=distance/speed

=250km/13.33km/min

=18.75 min

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