Problem 40 What is an echo?... [FREE SOLUTION]

Chapter 5: Problem 40

What is an echo?

Short Answer

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Provide an example of an echo with a calculation of the time delay. Answer: An echo is a reflection of sound off a solid surface that reaches the listener after a delay. The delay is determined by the distance between the sound source and the reflecting surface, as well as the speed of sound in the medium. In the example of a person clapping their hands 50 meters away from a wall and assuming the speed of sound in air is 340 meters per second, the time delay for the echo can be calculated as (2 x 50)/340 鈮� 0.29 seconds. The person would hear the echo approximately 0.29 seconds after the direct sound.

Step by step solution

Understanding sound and its properties

Sound is a vibration that travels through a medium, like air or water. It is a type of mechanical wave, which means that it moves through the medium by displacing the particles in the medium. The speed at which sound travels through a medium depends on the properties of that medium.

Defining an echo

An echo is a sound that is reflected off a solid surface and reaches the listener after a delay. When a sound wave encounters a surface, some of the sound energy is reflected back towards the source, while the rest is absorbed by the surface or transmitted through it. The reflected sound wave that travels back to the listener is called an echo.

Understanding the delay in an echo

The delay between the direct sound and its echo depends on the distance between the sound source and the reflecting surface, as well as the speed of sound in the medium. The total distance traveled by the sound wave before reaching the listener as an echo is twice the distance between the sound source and the reflecting surface (assuming the listener is at the sound source). The time it takes for the sound wave to travel this distance can be found using the formula: Time = \frac{2 \times distance}{speed \, of \, sound}

Example of an echo

Imagine someone standing in front of a large wall, 50 meters away from it, and clapping their hands. The sound of the clap travels through the air, hits the wall, and then reflects back to the person. If we assume the speed of sound in air is approximately 340 meters per second, we can use the formula from Step 3 to calculate the time delay for the echo: Time = \frac{2 \times 50}{340} = \frac{100}{340} \approx 0.29 \, seconds So, the person would hear the echo of their clap approximately 0.29 seconds after hearing the direct sound.

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Key Concepts

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

Sound Waves

Sound waves are a type of energy transfer that involves the movement of particles in a medium such as air, water, or solids. These waves are longitudinal mechanical waves, meaning the particle displacement happens in the direction of the wave movement. This is similar to a slinky spring being pushed and pulled.

When you make a sound, like clapping your hands, it creates vibrations in the air. These vibrations are transmitted to nearby particles, causing them to vibrate as well. This chain reaction continues until the sound reaches your ears.

The vibrations cause regions of compression and rarefaction in the medium.
Sound waves can also vary in frequency and wavelength, affecting the pitch and volume of the sound you hear.
Sound cannot travel in a vacuum because there are no particles to transmit the vibrations.

Reflection of Sound

Reflection of sound occurs when sound waves encounter a barrier or surface and bounce back. This process is quite similar to the reflection of light. When sound is reflected, some of its energy returns back towards the source, while other parts may be absorbed by the surface or transmitted through it.

Reflected sound waves are what produce echoes. An echo occurs when the delay between the original sound and its reflection is noticeable, which typically requires a significant distance between the sound source and the reflecting surface. That distance needs to be long enough so the ear can distinguish between the two sounds.

If objects absorb too much sound, like carpets and curtains in a room, echoes are reduced significantly.
Materials and angles of surfaces influence how sound waves are reflected.
Smooth and hard surfaces tend to reflect sound more effectively than rough and soft surfaces.

Speed of Sound

The speed of sound is how fast sound waves travel through a medium. It varies depending on the medium's properties, such as its density and temperature. In air, the speed of sound is approximately 340 meters per second at room temperature, but this can increase in more rigid materials like metal or water, where particles are closer together.

Factors that affect the speed of sound include:

Medium Type: Sound travels faster in solids because particles are more tightly packed than in liquids or gases.
Temperature: Higher temperatures increase the speed of sound as particles move more rapidly.
Air Pressure: While air pressure itself has minor effects compared to temperature and humidity, at constant density conditions, lower pressure can increase speed slightly.

Understanding the speed of sound helps in calculating the delay of echoes, as seen in the example calculation of an echo in air.

Mechanical Waves

Mechanical waves are waves that require a medium to travel through. Sound waves fall into this category because they need air, water, or another substance to carry the vibration from the source to the listener.

There are two primary types of mechanical waves: transverse and longitudinal. Sound waves, specifically, are longitudinal waves. Here's how they are characterized:

Longitudinal Waves: In these, the particles in the medium move parallel to the direction of the wave. Imagine making a ripple in a slinky by compressing one end.
Transverse Waves: In contrast, particles move perpendicular to the wave direction, like waves on a string.
In all cases, mechanical waves result from a source of disturbance, like striking a tuning fork, that creates energy which is transferred through a medium.

Mechanical waves, including sound waves, highlight the importance of medium in sound transmission and provide a deeper understanding of phenomena like echoes.

91影视

What is an echo?

Short Answer

Step by step solution

Understanding sound and its properties

Defining an echo

Understanding the delay in an echo

Example of an echo

Key Concepts

Sound Waves

Reflection of Sound

Speed of Sound

Mechanical Waves

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