# Resonance, standing waves and bass

In summary, the sound waves in a room become louder if you are close to any of the walls. The wall reflections do not cancel the instantaneous pressure of the sound wave, so the air pressure oscillations make the walls resonate.
Why is it that in a room, if you're close to any of the walls the lower frequencies of a sound become louder? Ofcourse, there's an interference pattern in the room. You can hear this by walking around and you'll notice that at some points the bass is weaker and at some points it's stronger (the nodes and antinodes are easier to pinpoint in the longer wavelengths). But shouldn't there be nodes at the walls and hence the level would drop there? Instead, there's a remarkable increase in bass level if you get within, say, 0.5 meters from a wall.

the reflection on a hard wall does not cancel the instantaneous pressure of the sound wave at the positions of the wall. theoretically (let's say its a very thick and perfectly flat wall of polished marble), it does cancel the component of the particle velocity that is perpendicular to the surface of the wall at that surface. for a single and infinite flat wall in infinite space (with air) and a single source located some given distance away from the wall, the solution to the wave equation (of sound in air) with that flat wall imposing the boundary condition above (that the particle velocity perpedicular to the wall is zero at the surface of the wall) is identical to the solution of empty air space with that same sound source and a mirror image sound source (with a perfectly in-phase coherent wave) that would be located behind the wall at the reflected position. the two sources (the real and phantom source) would, at the points where the wall's surface used to be, cancel out the component of particle velocity that is perpendicular to the wall surface. but the instantaneous pressure would team up (constructive interference).

now, what do you think will happen as you get closer to the wall's surface if they team up at the surface?

Ok, so does that mean that the air pressure oscillations make the walls resonate? Otherwise, I don't see where the frequency dependence comes from?

## What is resonance?

Resonance is a phenomenon that occurs when a system is subjected to a periodic force at the same frequency as its natural frequency. This causes the system to vibrate with a higher amplitude, resulting in a buildup of energy.

## What are standing waves?

Standing waves are a type of wave pattern that forms when two waves of the same frequency and amplitude travel in opposite directions and interfere with each other. They appear to be stationary, with nodes and antinodes that do not move.

## How do standing waves relate to resonance?

Resonance can occur in a system when it is subjected to standing waves. This is because the standing waves have the same frequency as the natural frequency of the system, causing it to vibrate with a higher amplitude.

## What is the role of bass in resonance?

Bass, which refers to low frequency sound waves, can play a crucial role in resonance. This is because low frequencies have longer wavelengths, allowing them to create larger standing waves and induce stronger resonance in a system.

## How can resonance and standing waves affect musical instruments?

Resonance and standing waves are essential in creating sound in musical instruments. For example, the strings of a guitar or violin vibrate at their natural frequency, producing a standing wave that resonates within the instrument and amplifies the sound. The shape and size of the instrument also affect the standing waves and the resulting sound produced.

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