An ultrasonic ruler displays the distance between the ruler and an object, such

Question

An ultrasonic ruler displays the distance between the ruler and an object, such as a wall. The ruler sends out a pulse of ultrasonic sound and measures the time it takes for the pulse to reflect from the object and return. The ruler uses this time, along with a preset value for the speed of sound in air, to determine the distance. Suppose that you use this ruler under water, rather than in air. The actual distance from the ultrasonic ruler to an object is 22.0 m. The adiabatic bulk modulus and density of seawater are Bad = 2.37 × 109 Pa and = 1025 kg/m3, respectively. Assume that the ruler uses a preset value of 343 m/s for the speed of sound in air. Determine the distance reading that the ruler displays.

Explanation / Answer

given,

bulk modulus B=2.37*10^9 pa

density rho=1025 kg/m^3

speed of the sound in water v_water=sqrt(B/rho)

V=sqrt(2.37*10^9/1025)

=1520.6 m/sec

and

time taken t=total distance/V_water

=(22)/1520.6

=14.468 m.sec

and

given,

speed of the sound in air, v_air=343 m/sec

and t=14.468 m.sec

now,

reading value on the ruler is , distance x=V_air*t

=343*14.468*10^-3

=4.96 m

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