18. Waves & Sound

(II) A tight guitar string has a frequency of 540 Hz as its third harmonic. What will be its fundamental frequency if it is fingered at a length of only 70% of its original length?

An old mining tunnel disappears into a hillside. You would like to know how long the tunnel is, but it's too dangerous to go inside. Recalling your recent physics class, you decide to try setting up standing-wave resonances inside the tunnel. Using your subsonic amplifier and loudspeaker, you find resonances at 4.5 Hz and 6.3 Hz, and at no frequencies between these. It's rather chilly inside the tunnel, so you estimate the sound speed to be 335 m/s . Based on your measurements, how far is it to the end of the tunnel?

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 the fundamental frequency?

A 1.0-m-tall vertical tube is filled with 20°C water. A tuning fork vibrating at 580 Hz is held just over the top of the tube as the water is slowly drained from the bottom. At what water heights, measured from the bottom of the tube, will there be a standing wave in the tube above the water?

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

(II) An unfingered guitar string is 0.68 m long and is tuned to play E above middle C (330 Hz). What is the wavelength on the string of this 440-Hz wave?

A space probe enters the thin atmosphere of a planet where the speed of sound is only about 55 m/s. What is the angle of the shock wave relative to the direction of motion?

A pipe in air at 21.5°C is to be designed to produce two successive harmonics at 308 Hz and 352 Hz. How long must the pipe be, and is it open or closed?

(II) A meteorite traveling 9400 m/s strikes the ocean. Determine the shock wave angle it produces in the water just after entering. Assume T = 20 °C.

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?

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 the speed of sound in the gas in the tube?