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Dolphins emit clicks of sound for communication and echolocation. A marine biologist is monitoring a dolphin swimming in seawater where the speed of sound is 1522 m/s. When the dolphin is swimming directly away at 8.0 m/s, the marine biologist measures the number of clicks occurring per second to be at a frequency of 2500 Hz. What is the difference (in Hz) between this frequency and the number of clicks per second actually emitted by the dolphin?

Short Answer

Expert verified
The difference is approximately 13.13 Hz.

Step by step solution

01

Identify the Known Values

We know the speed of sound in seawater is \(v = 1522 \text{ m/s}\) and the speed of the dolphin is \(v_s = 8.0 \text{ m/s}\). The observed frequency of clicks is \(f' = 2500 \text{ Hz}\).
02

Understand the Doppler Effect for Sound

The Doppler Effect equation for sound moving away from an observer is given by: \[ f' = \left( \frac{v}{v+v_s} \right) f \] where \(f\) is the frequency of sound emitted by the source.
03

Rearrange the Equation to Solve for Emitted Frequency

Rearrange the Doppler Effect equation to find \(f\), the emitted frequency: \[ f = f' \times \frac{v+v_s}{v} \]
04

Substitute Known Values into the Equation

Substitute the known values into the rearranged equation: \[ f = 2500 \times \left( \frac{1522 + 8}{1522} \right) \]
05

Calculate the Emitted Frequency

Calculate the emitted frequency using the equation from Step 4: \[ f = 2500 \times \left( \frac{1530}{1522} \right) \approx 2500 \times 1.00525 \approx 2513.13 \text{ Hz} \]
06

Determine the Frequency Difference

Find the difference between the emitted frequency and the observed frequency: \[ \Delta f = f - f' = 2513.13 - 2500 = 13.13 \text{ Hz} \]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Frequency Calculation
Frequency calculation is crucial in understanding the changes in sound perception caused by motion. When moving objects emit sound, the frequency of the observed sound can differ from the original frequency emitted. This phenomenon is at the heart of our exercise. The observed frequency ( f' ) is given, and we need to find the frequency actually emitted by the dolphin ( f ).
We use the Doppler Effect formula: \[ f' = \left( \frac{v}{v+v_s} \right) f \] This formula applies when the sound source is moving away from the observer. By rearranging it to solve for ( f ), and substituting the known values, we calculate \[ f = 2500 \times \left( \frac{1530}{1522} \right) \approx 2513.13 \text{ Hz} \].
This provides the emitted frequency. To find the frequency difference, subtract the observed frequency from this value, yielding a \( \Delta f = 13.13 \text{ Hz} \).
Frequency calculation like this helps us understand dynamic acoustic environments, especially in marine biology, where motion can significantly alter perceived sounds.
Sound Waves
Sound waves are vibrations that travel through a medium, such as air or water. They are characterized by parameters like wavelength, speed, and frequency. In water, sound travels faster than in air. Here, the speed of sound in seawater is 1522 m/s.
When a dolphin emits clicks, these clicks propagate as sound waves. As the dolphin moves, the characteristics of these waves change for an observer. This change is due to the Doppler Effect, a crucial concept for understanding sound wave behavior in moving systems.
Sound waves carry energy and information. In the context of marine biology, they enable dolphins to communicate and navigate their environment effectively. Understanding the behavior of sound waves in water is vital for interpreting the changes in frequency and for dolphins' successful interaction with their surroundings.
Marine Biology
Marine biology is the study of life in aquatic environments. It covers everything from microscopic organisms to large mammals like dolphins. A significant aspect of marine biology involves understanding the interaction between marine organisms and their environment, including how they utilize sound.
Dolphins are fascinating subjects in marine biology due to their complex communication methods and echolocation abilities. These marine mammals emit sound waves to navigate and communicate. Sound travels efficiently in water, making it an excellent medium for such purposes.
  • Understanding the speed of sound and its interaction with marine life enhances our knowledge of dolphin behavior.
  • Observational studies, like the one in our exercise, help researchers understand these interactions better.
Understanding sound perception differences, due to effects like the Doppler Effect, is a key component in the study of marine biology and helps researchers in effective monitoring of aquatic creatures.
Echolocation
Echolocation is an amazing biological sonar used by various animals, including dolphins. It involves emitting sound waves and interpreting the echoes that return from objects. This process helps dolphins "see" their surroundings even in murky waters.
Here's how echolocation works:
  • A dolphin emits a series of clicks.
  • These clicks travel as sound waves until they hit an object.
  • The sound waves then bounce back as echoes, which the dolphin interprets to determine the object's distance and shape.
This exercise highlights how echolocation is impacted by the Doppler Effect. The frequency of the returning sound waves can change if the dolphin or the observed object is moving. Such knowledge allows marine biologists to understand and measure these effects, contributing to more profound insights into dolphin behavior and communication mechanisms.

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Most popular questions from this chapter

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