On a guitar, there are six strings, all the same length. However. all of these s

Question

On a guitar, there are six strings, all the same length. However. all of these strings play different pitches: the thick strings will play low pitches, and the thin strings will play high pitches. How do the speeds of the waves in these strings compare? Explain your reasoning. While playing guitar, you notice that there is a fret (a ridge used by the guitarist to "pin down" a string) ex-actly halfway between the nut and the saddle (see diagram to the right). If you press down on this fret and pluck the string, how will the pitch compare to that of the open string if the open string plays an A (frequency 110 Hz)? Explain why this happens.

Explanation / Answer

We know that, wave speed is given as:
v= Sqrt(T/n) where, T= Tension in the string and n= mass per unit length of string
Hense,
n varies in each string. Although the length is same in each case but mass in each case is different. That's why the value of n is maximum in thick string and hense,its wave speed is lowest which results in low pitch.
On the other hand,the value of n is minimum in thin string and hense,its wave speed is highest which results in high pitch.

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