dolphins of the open ocean are classified as type ii odontocetes (toothed whales). these animals use ultrasonic \clicks\ with a frequency of about $55\text{ khz}$ to navigate and find prey.

part a
suppose a dolphin sends out a series of clicks that are reflected back from the bottom of the ocean $90\text{ m}$ below. how much time elapses before the dolphin hears the echoes of the clicks? (the speed of sound in seawater is approximately $1530\text{ m/s}$.)
express your answer in seconds.

part b
what is the wavelength of $55\text{ khz}$ sound in the ocean?
express your answer in millimeters.

Question

dolphins of the open ocean are classified as type ii odontocetes (toothed whales). these animals use ultrasonic \clicks\ with a frequency of about $55\text{ khz}$ to navigate and find prey.

part a
suppose a dolphin sends out a series of clicks that are reflected back from the bottom of the ocean $90\text{ m}$ below. how much time elapses before the dolphin hears the echoes of the clicks? (the speed of sound in seawater is approximately $1530\text{ m/s}$.)
express your answer in seconds.

part b
what is the wavelength of $55\text{ khz}$ sound in the ocean?
express your answer in millimeters.

Accepted Answer

{ "quality": "clear", "question_count": 2, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Wave Speed Formula", "Wavelength Definition" ], "new_concepts": [ "Echo Time Calculation" ], "current_concepts": [ "Wave Speed Formula", "Wavelength Definition", "Echo Time Calculation" ] } ## Calculate elapsed time for the echo in Part A $$ \begin{aligned} d_{\text{total}} &= 2 \times d = 2 \times 90\text{ m} = 180\text{ m} \ v &= 1530\text{ m/s} \ t &= \frac{d_{\text{total}}}{v} = \frac{180\text{ m}}{1530\text{ m/s}} \approx 0.1176\text{ s} \approx 0.12\text{ s} \end{aligned} $$ ## Calculate wavelength in Part B $$ \begin{aligned} f &= 55\text{ kHz} = 55000\text{ Hz} \ v &= 1530\text{ m/s} \ \lambda &= \frac{v}{f} = \frac{1530\text{ m/s}}{55000\text{ Hz}} \approx 0.02782\text{ m} \ \lambda_{\text{mm}} &= 0.02782\text{ m} \times 1000\text{ mm/m} \approx 28\text{ mm} \end{aligned} $$ ## Question 1 $t = 0.12$ s ## Question 2 $\lambda = 28$ mm { "subject": "Natural Science", "question_type": "Multi-part", "knowledge_point": [ "Natural Science", "Physics", "Wave Speed Formula" ] }

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QUESTION IMAGE

Question

Explanation:

Calculate elapsed time for the echo in Part A

Calculate wavelength in Part B

Answer:

Question 1

Question 2