Question

On a guitar, there are six strings, all the same length. How- ever, 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.

Answer 1

The guitar strings satisfy the relation between wavelength and frequency

i,e v=fλ

f=v/λ

i,e frequency of the wave is dependent on both the speed of the wave and the length of the wave

Speed of the wave in guitar depends on the tension of the string and the linear mass density

$v=\sqrt{T/\mu }$

so waves will travel slower on a more massive string , if the mass is increased, the v will decrease. if mass is decreased speed of wave increases

We know that high frequency produces high pitch. so frequency and velocity is propotional , and velocity of wave decreases pitch also decreases. (for thick strings)

for thin springs velocity increases and frequency raises and cause high pitch