Question

A person blows into open-end of a long pipe. As a result, a high-pressure pulse of air travels down the pipe. When this pulse reaches the other end of the pipe, (A) a high-pressure pulse starts traveling up the pipe, if the other end of the pipe is open. (B) a low-pressure pulse starts traveling up the pipe, if the other end of the pipe is open. (C) a low-pressure pulse starts traveling up the pipe, if the other end of the pipe is closed. (D) a high-pressure pulse starts traveling up the pipe, if the other end of the pipe is closed.

Short answer

The correct answers are (A) a high-pressure pulse starts traveling up the pipe, if the other end of the pipe is open, and (C) a low-pressure pulse starts traveling up the pipe, if the other end of the pipe is closed.

Step-by-step solution

Understand the Behavior of Waves in Pipes

Recognize that within a pipe, a pulse of air creates a wave that reflects back from the end of the pipe. The nature of the reflection depends on whether the end is open or closed. An open end is a pressure-release boundary which generally reflects the wave with the same pressure profile, while a closed end is a fixed boundary which reflects the wave with an inverted pressure profile.

Determine the Reflection at an Open End

Apply the principle that an open end is a pressure-release boundary. When a high-pressure pulse reaches it, the pulse is reflected back down the pipe without inverting, resulting in another high-pressure pulse traveling back.

Determine the Reflection at a Closed End

Understand that a closed end acts as a fixed boundary, differing from an open end. When the high-pressure pulse hits a closed end, it is reflected with a pressure inversion, which means the reflected wave will be a low-pressure pulse.

Key concepts

Behavior of Waves

Understanding the behavior of waves in a confined space, such as a pipe, lays the foundation for a plethora of applications in physics, ranging from musical instruments to industrial pipes. When a wave encounters a boundary, reflection occurs—this is a fundamental property of waves. In a pipe, a pressure pulse is effectively a longitudinal wave, characterized by regions of high and low pressure moving through the air inside the pipe.

As this pulse travels, the behavior upon reaching the end of the pipe is critical to its subsequent motion. If the wave encounters a sudden change in medium or a boundary (like an end of the pipe), parts of the wave are reflected back towards the source. The characteristics of this reflection—whether it's direct or inverted—depend on the conditions at the boundary, which could be open or closed in the case of a pipe.

Open-End Reflection

When dealing with an open-end reflection, imagine the end of a pipe opening into a vast space. The boundary here is called a 'pressure-release boundary'. The air atoms have more freedom to move at this open end and are not constrained as they would be by a wall or a closed end. Consequently, if a high-pressure pulse arrives at an open end, physics tells us that it will be reflected back without changing its character. This means that the high-pressure areas remain high-pressure upon reflection.

For instance, when blowing into an open pipe, a high-pressure pulse forms and travels until it reaches the open end. Upon reflection at this pressure-release boundary, it retains its pressure profile and creates another high-pressure pulse moving in the opposite direction. This observation directly relates to the sound properties of wind instruments such as flutes where sound waves reflect inside an open-ended cylindrical tube.

Closed-End Reflection

Closed-end reflection provides a contrasting scenario to an open end. A closed end acts as a 'fixed boundary', where the air molecules cannot move freely past the end. In this case, the behavior of the wave upon reflection is quite different. When a high-pressure pulse strikes a closed end, it encounters a rigid barrier.

Due to the lack of freedom for the air molecules' motion, the wave undergoes an inversion process, swapping regions of high and low pressure. This results in a wave inversion, where a high-pressure pulse reflects as a low-pressure pulse. These principles underpin various acoustical phenomena and are critical in understanding how sound waves behave in environments with one or more closed boundaries — like the body of a guitar or the exhaust system on a car.

Pressure Pulse

A pressure pulse in the context of a pipe is a surge of air molecules. This can be visualized as a domino effect, where each molecule pushes its neighbor forward, creating a region of compression followed by a region of rarefaction. This pulse is responsible for initiating the wave motion inside the pipe, where its subsequent reflections depend on the boundary conditions at the pipe's ends.

The concept of a pressure pulse is a crucial component of wave dynamics, particularly in fluids and gases. Pressure pulses are not only central to understanding acoustics but also play significant roles in technologies like pipelines, pneumatic systems, and even medical devices such as stethoscopes.

Wave Inversion

Wave inversion is a fascinating phenomenon that occurs during the reflection of waves. It happens when a wave that has a certain characteristic, such as being a high-pressure pulse, reflects off a boundary and comes back with an opposite characteristic—turning into a low-pressure pulse in the case of a closed-end reflection.

This change is not random but follows physical laws where fixed boundaries result in such an inversion. Understanding wave inversion is essential for many applications, including noise cancellation technologies where inverted sound waves are used to reduce unwanted noise, and for diagnosing issues within pipe systems by analyzing how pressure pulses reflect and invert.