Why do large objects produce bass sound?

For example a large area sheet of linoleum can be a good radiator of bass or a good receiver or absorber of bass.

A large grand piano may be a great deep bass sound radiator. It has a large area soundboard and long strings.


A large member of the string instrument family eg a double bass which is big radiates bass.


Long strings produce or receive bass.


But why?


Use of wavelength will be deliberately omitted. Instead first principles will be a guide.


For example the basic fact that the longer the distance a wave travels the longer the time it takes.


And the fundamental theorem of impedance matching. When we have impedance mismatch a wave is reflected back. For example a ball hitting a wall and bouncing back. By the way a ball hitting a linoleum wall does not come back, energy is absorbed by linoleum. This can be thought as an impedance match condition.
When impedances are matched energy is not reflected back. It is either absorbed or transmited. For example if a wave keeps traveling in the same medium (eg water) it keeps traveling until wave finds an obstacle (impedance mismatch).


A swimming pool is a nice example.


We just throw a pebble on the calm water.


A concentric wave can be seen expanding. Circles get bigger and bigger. This is because the wave travels in all directions as there is symmetry.


When water wave finds an obstacle of impedance mismatch ie a wall of the swimming pool, it is reflected back.


Gradually the wave will be reflected back at all directions as it will hit all sides of swimming pool. The wave will move towards the inner part of the swimming pool. It will re-reflect again as it arrives again on swimming pool boundary walls.


Clearly the longer the dimensions of the swimming pool the longer it takes for this periodic phenomenon to repeat. This means a low frequency.


What we humans perceive as bass.


Exactly the same happens on a string. It is actually simpler as this is a wave travelling in one dimension. Inside a piano or a guitar string a wave travels along its length. When it finds a discontinuity, for example the fret that our finger is pressing, it is reflected back. When it then meets while still traveling the bridge of the guitar, it is again reflected back. This oscillation back and forth is what creates the musical note, the sound. For example on guitar the 1 dimensional vibration is converted to 2 dimensional. How? Each time the string wave is reflected from the guitar bridge, some of it's energy is transfered trough the bridge to the thin surface area of wooden soundboard. The soundboard behaves like the surface of the water in the swimming pool. The soundboard vibrates. It's vibration can be felt if we touch it while a string is vibrating. The vibration of the soundboard sets by collision the vibration of nearby air molecules. These molecules collide with their neighbours and now a wave travelling in 3 dimensions is created. Such energy transfer carries on. Vibrating molecules near our eardrum collide with it and the vibration is transfered to it. We can then hear the sound. Actually molecule collision is an electric force phenomenon. Atoms cannot touch each other as negative charge electrons of one atom close to negative charge electrons of another atom repel each other. This is in fact what makes us float in water when we swim. Water molecules never touch our body molecules. They just come too close that the total repulsive force is strong enough to keep us floating.


Now back to 1 dimension. For example when we shorten the length of a guitar say by pressing string on a fret, frequency increase (the wave comes quicker back and forth) and we humans perceive a higher note pitch.

We c
behaves like Same with a drum skin in 2 dimensions.


Same with a big cathedral in 3 dimensions.


Same with a linoleum sheet in 2 dimensions. As the wave travels inside linoleum it keep going and when the wave reach the end or boundary of linoleum it reflects back. Linoleum has also the property of converting the wave vibration of its structure to heat. Thereby damping oscillation or absorbing the energy of the wave. This property can be useful as absorber or uncolored radiator of bass ie low frequecy. See next posts.



See also:


Musical Acoustics - Donald Hall


Acoustics of Radio and Television Studios - Christoher Gilford - BBC


The Feynman Lectures on Physics