Question

A fish finder uses a sonar device that sends 20,000 Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 85 m, what is the minimum time between pulses (in fresh water)?

Short answer

The minimum time between pulses is \(0.12\;{\rm{s}}\).

Step-by-step solution

Determination of speed of moving system

The velocity of the moving system is the fraction of the total distance traveled to the time of journey. There is an inverse relationship between the velocity and the elapsed time.

Given information

Given data:

The frequency of sound sends by device is \(f = 20,000\;{\rm{Hz}}\).

The maximum depth is \(h = 85\;{\rm{m}}\).

The standard value for the speed of sound in water from Table 12-1 is \(1440\;{{\rm{m}} \mathord{\left/{\vphantom {{\rm{m}} {\rm{s}}}} \right.} {\rm{s}}}\).

Evaluate the minimum time between the pulses

The minimum time between pulses is calculated below:

\(\begin{aligned}{c}v = \frac{d}{t}\\t = \frac{d}{v}\\ = \frac{{2h}}{v}\end{aligned}\)

Substitute the values in the above equation.

\(\begin{aligned}{l}t &= \frac{{2\left( {85\;{\rm{m}}} \right)}}{{\left( {1440\;{{\rm{m}} \mathord{\left/{\vphantom {{\rm{m}} {\rm{s}}}} \right.} {\rm{s}}}} \right)}}\\t &= 0.12\;{\rm{s}}\end{aligned}\)

Hence, the minimum time between pulses is \(0.12\;{\rm{s}}\).