A musician is setting up a cello to play a concert.
Explain how a stationary wave is produced when a cello string is bowed or plucked.
The vibrating length of a particular cello string is 0.60 m0.60 \text{ m}0.60 m. When the tension in this string is 144 N144 \text{ N}144 N, the string vibrates with a first-harmonic frequency of 120 Hz120 \text{ Hz}120 Hz.
Calculate the mass of a 1.0 m1.0 \text{ m}1.0 m length of this string.
Determine the speed at which waves travel along this string when it vibrates with a first-harmonic frequency of 120 Hz120 \text{ Hz}120 Hz.
The tension in the string is directly proportional to its extension, with a stiffness (force per unit extension) of 16 N mm−116 \text{ N mm}^{-1}16 N mm−1. The musician tunes the cello to a higher pitch by rotating a circular tuning peg of diameter 6.0 mm6.0 \text{ mm}6.0 mm through an angle of 60∘60^\circ60∘. Determine the new higher first-harmonic frequency produced. Assume that there is no change in the mass per unit length of the string.