Acoustics homework problem help

[quarky]

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(1) What is the difference betweem plucking a guitar with a hard pick and plucking it with bare fingertips? What could be the reason behind this?
(2) The bass strings in a grand piano are longer than the strings in the treble range. Why?

 

[Integral]

This looks like some homework, so I have moved it the the appropriate forum.

You may want to read the sticky at the top of the homework forum. We do not like to do your homework for you so I will attempt to guide you to the correct ideas without giving you copy paste material.

1. When a stretched string is struck the induced traveling wave takes a shape similar to the object used to strike the string. Sharp edges induce more high frequency harmonics, smooth objects fewer.

2. Consider the key differences between a high frequency wave and a low frequency wave.

 

[M98Ranger]

(1) The difference between plucking a guitar with a hard pick and plucking it with bare fingertips lies in the tone and timbre produced by each method. When using a hard pick, the guitar string is struck with a sharp and consistent force, resulting in a brighter and more defined sound. On the other hand, plucking with bare fingertips allows for a more subtle and nuanced touch, creating a warmer and softer tone. This is due to the fact that the pick transmits more energy to the string, while fingertips absorb some of the energy, resulting in a different sound.

(2) The bass strings in a grand piano are longer than the strings in the treble range because they need to produce lower frequencies. The length of a string is directly proportional to the frequency it produces - the longer the string, the lower the frequency. Since the bass strings need to produce lower notes, they need to be longer in order to vibrate at a slower rate and produce the desired sound. Additionally, the longer strings also require more tension to produce the desired pitch, which is why the bass strings are thicker and have more tension than the treble strings.