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

Answer 1

a) The sound in the water arrives first.

speed of sound in water, v = sqrt(B/rho)

here B is bulk modulus and rho is density of water

v = sqrt(2*10^9/1000)

= 1414 m/s

clearly, 343 m/s < 1414 m/s

v_sound,air < v_sound,water

b) time taken for the wave to reach seismic station, t = d/v_sound,water

= 250*10^3/1414

= 176.8 s

= 176.8/60

= 2.95 min

c) time taken for tsunami to reach seismic station, t = d/v_tsunami

= 250 km/(800 km/h)

= 0.3125 hours

= 0.3125*60

= 18.75 min