18. Waves & Sound

(II) An unfingered guitar string is 0.68 m long and is tuned to play E above middle C (330 Hz).

(a) How far from the end of this string must a fret (and your finger, Fig. 16–8) be placed to play A above middle C (440 Hz)?

(II) A uniform narrow tube 1.50 m long is open at both ends. It resonates at two successive harmonics of frequencies 275 Hz and 330 Hz. What is

(b) the speed of sound in the gas in the tube?

(II) A space probe enters the thin atmosphere of a planet where the speed of sound is only about 55 m/s .

(b) What is the angle of the shock wave relative to the direction of motion?

A particular whistle produces sound by setting up the fundamental standing wave in an air column 8.40 cm long. The tube is closed at one end. The whistle blower is riding in a car moving away from you at 25 m/s. What frequency do you hear?

The vibrating portion of an A-string on a particular violin measures 32 cm, and its fundamental frequency is precisely 440 Hz.

(a) How far from the end of the string should the violinist place a finger so that the string plays a note at 588 Hz?

The vibrating portion of an A-string on a particular violin measures 32 cm, and its fundamental frequency is precisely 440 Hz.

(b) “Vibrato” in a violin is produced by sliding the finger back and forth along the vibrating string. If the violinist executes “vibrato” by moving the finger 0.5 cm to either side of the position found in part (a), what range of frequencies will result?