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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?

Respuesta :

Answer:

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

b) [tex] 2d = v t [/tex]

If we solve for d we got:

[tex] d = \frac{vt}{2}[/tex]

And we can replace the values given and we got:

[tex] d = \frac{1480 m/s*0.42s}{2}=310.8 m[/tex]

Explanation:

Part a

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

[tex] v = \lambda f[/tex]

If we solve for the wavelength we got:

[tex] \lambda = \frac{v}{f}[/tex]

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:

[tex] f= 600 kHz *\frac{1000 Hz}{1 kHz}= 600000 Hz[/tex]

And now if we find the wavelength we got:

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

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:

[tex] D = vt[/tex]

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

[tex] 2d = v t [/tex]

If we solve for d we got:

[tex] d = \frac{vt}{2}[/tex]

And we can replace the values given and we got:

[tex] d = \frac{1480 m/s*0.42s}{2}=310.8 m[/tex]

(a) The wavelength of the wave is 2.24 mm

(b) The depth of the shipwreck is 320.8 m

Wavelength:

(a) The wavelength of a wave is the smallest distance between two points that are in the same phase. Mathematically the wavelength (λ), frequency (f) and velocity (v) of the wave are related as follows:

[tex]v=\lambda f[/tex]

the speed of sound in water is v = 1480m/s and the given frequency is 600kHz, so:

[tex]\lambda=\frac{v}{f}=\frac{1480}{660\times10^3}\\\\\lambda=2.24\;mm[/tex]

(b) the echo travels two times the depth (d) of the shipwreck, so

[tex]2d=vt\\\\d=\frac{vt}{2}\\\\d=\frac{1480\times0.42}{2}\\\\d=310.8\;m[/tex]

learn more about wavelength:

https://brainly.com/question/7143261?referrer=searchResults

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