Question

Research vessels at sea can create images of their surroundings by sending out sound waves and measuring the time until they detect echoes. This image of a shipwreck on the ocean bottom was made from the surface with 600 kHz ultrasound.
a. What was the wavelength?
b. How deep is the shipwreck if echoes were detected 0.42 s after the sound waves were emitted?

Answer 1

Answer:

a) $\lambda = \frac{1480 m/s}{600000 Hz}= 0.00246 m * \frac{1000 mm}{1m}= 2.47 mm$

b) $2d = v t$

If we solve for d we got:

$d = \frac{vt}{2}$

And we can replace the values given and we got:

$d = \frac{1480 m/s*0.42s}{2}=310.8 m$

Explanation:

Part a

For this case if we have a fundamental wave we need to satisfy the following relationship:

$v = \lambda f$

If we solve for the wavelength we got:

$\lambda = \frac{v}{f}$

We know that the velocity of the sound in water is different from air and is approximately 1480 m/s.

We can convert the frequency given into Hz like this:

$f= 600 kHz *\frac{1000 Hz}{1 kHz}= 600000 Hz$

And now if we find the wavelength we got:

$\lambda = \frac{1480 m/s}{600000 Hz}= 0.00246 m * \frac{1000 mm}{1m}= 2.47 mm$

Part b

For this case the time given t =0.42 seconds represent the time required in order to the wave go and return to the device. So the total distance would be 2d, where d represent the depth.

We know that from kinematics:

$D = vt$

Where D is the distance, v the velocity and t the time. If we use this relation we have:

$2d = v t$

If we solve for d we got:

$d = \frac{vt}{2}$

And we can replace the values given and we got:

$d = \frac{1480 m/s*0.42s}{2}=310.8 m$