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Chapter 17: Q4. (page 482)
An organ pipe is tuned to exactly 384 Hz when the room temperature is 20掳C. If the room temperature later increases to 22掳C, does the pipe鈥檚 frequency increase, decrease, or stay the same? Explain.
Pipe's frequency will increase
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A string vibrates at its third-harmonic frequency. The amplitude at a point 30 cm from one end is half the maximum amplitude. How long is the string?
We can make a simple model of the human vocal tract as an open-closed tube extending from the opening of the mouth to the diaphragm. What is the length of this tube if its fundamental frequency equals a typical speech frequency of 250 Hz? The speed of sound in the warm air is 350 m/s.
Deep-sea divers often breathe a mixture of helium and oxygen to avoid getting the 鈥渂ends鈥� from breathing high-pressure nitrogen. The helium has the side effect of making the divers鈥� voices sound odd. Although your vocal tract can be roughly described as an open-closed tube, the way you hold your mouth and position your lips greatly affects the standing-wave frequencies of the vocal tract. This is what allows different vowels to sound different. The 鈥渆e鈥� sound is made by shaping your vocal tract to have standing- wave frequencies at, normally, 270 Hz and 2300 Hz. What will these frequencies be for a helium-oxygen mixture in which the speed of sound at body temperature is 750 m/s? The speed of sound in air at body temperature is 350 m/s.
An old mining tunnel disappears into a hillside. You would like to know how long the tunnel is, but it鈥檚 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鈥檚 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?
As the captain of the scientific team sent to Planet Physics, one
of your tasks is to measure g. You have a long, thin wire labeled
1.00 g/m and a 1.25 kg weight. You have your accurate space cadet
chronometer but, unfortunately, you seem to have forgotten a
meter stick. Undeterred, you first find the midpoint of the wire by
folding it in half. You then attach one end of the wire to the wall
of your laboratory, stretch it horizontally to pass over a pulley at
the midpoint of the wire, then tie the 1.25 kg weight to the end
hanging over the pulley. By vibrating the wire, and measuring
time with your chronometer, you find that the wire鈥檚 second harmonic
frequency is 100 Hz. Next, with the 1.25 kg weight still
tied to one end of the wire, you attach the other end to the ceiling
to make a pendulum. You find that the pendulum requires 314 s to
complete 100 oscillations. Pulling out your trusty calculator, you
get to work. What value of g will you report back to headquarters?
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