Question

A guitar string is \[90cm\] long and has a fundamental frequency of \[124Hz\]. To produce a fundamental frequency of \[186Hz\], the guitar should be pressed at?
A. \[60cm\]
B. \[30cm\]
C. \[20cm\]
D. \[10cm\]

Answer 1

Hint: Here we can use the law of length. The law of length is outlined as A stretched string's vibration frequency varies reciprocally with its reverberant length (provided its mass per unit length and tension stay constant.). therefore if we all know the law of length means that, we can realize answers simply.

Formula used:
The law of length is, \[{v_2}{L_2} = {v_1}{L_1}\]
Here, \[{v_1}\& {v_2}\]- is the fundamental frequency produced by the guitar.
\[{L_1}\& {L_2}\]-is guitar string lengths.

Complete step by step solution:
The guitar string length \[{L_1} = 90cm\] and \[{v_1} = 124Hz\], \[{v_2} = 186Hz\]
We can modify the laws of length is written as,
\[{L_2} = \dfrac{{{v_1}{L_1}}}{{{v_2}}}\]
Substitute those values into the laws of length, we can get
\[{L_2} = \dfrac{{124 \times 90}}{{186}}\]
\[{L_2} = 60cm\]

Additional Information:
The moving string isn't solely possessed by laws of length. It conjointly possesses laws of tension and laws of mass (or) law of linear density. The laws of tension are painted as If the length and mass per unit length are unbroken constant, the elemental frequency of vibrations of a stretched string is directly proportional to the root of the applied stress. The laws of mass say as If the length and tension are command constant, the elemental frequency of vibration of a stretched string is reciprocally proportional to the root of its mass per unit length.

Note: We can state the law of length as, If tension and mass per unit length stay constant, the basic frequency of a string's vibrations is reciprocally proportional to its length. The guitar string forces the sound field to start vibrating at the same frequency because of the string. The sound field in flip forces surrounding air molecules into vibrational motion. Due to the massive floor place of the soundbox, more air molecules are set into vibrational motion. This produces a more audible sound.