The human ear canal is approximately 2.5 cm long. It is open to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal.

Suppose three tuning forks of frequencies 260 Hz, 262 Hz, and 266 Hz are available. What beat frequencies are possible for pairs of these forks sounded together?

You have three tuning forks with frequencies of 252 Hz, 256 Hz, and 259 Hz. What beat frequencies are possible with these tuning forks?

Human hearing. The human outer ear contains a more-or-less cylindrical cavity called the auditory canal that behaves like a resonant tube to aid in the hearing process. One end terminates at the eardrum (tympanic membrane), while the other opens to the outside. Typically, this canal is approximately $2.4 \mathrm{~cm}$ long.
(a) At what frequencies would it resonate in its first two harmonics?
(b) What are the corresponding sound wavelengths in part (a)?

An organ pipe is 1.5 m long and open at both ends. What are the first three harmonic frequencies of this pipe?

(a) How far apart are two layers of tissue that produce echoes having round-trip times (used to measure distances) that differ by $0.750\ \mu \mathrm{s}?$ (b) What minimum frequency must the ultrasound have to see detail this small?

The fundamental frequency of the longest pipe on an organ is 16.35 Hz. If the pipe is open at both ends, how long is the pipe?

At point $A, 3.0$ m from a small source of sound that is emitting uniformly in all directions, the sound intensity level is $53 \mathrm{~dB}$.
($c$) How far must you go so that the sound inten- sity level is one-fourth of what it was at $A$?

A uniform narrow tube 1.80 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?

At point $A, 3.0$ m from a small source of sound that is emitting uniformly in all directions, the sound intensity level is $53 \mathrm{~dB}$.
(b) How far from the source must you go so that the intensity is one-fourth of what it was at $A$?

Two violinists, one directly behind the other, play for a listener directly in front of them. Both violinists sound concert A ($440 \mathrm{~Hz}$). What is the smallest separation between the violinists that will produce destructive interference for the listener?

Four standing waves, labeled A through D, are described below. Rank the standing waves in order of increasing frequency. Indicate ties where appropriate. Wave A: first harmonic; pipe closed at one end; length =1 m Wave B: first harmonic; pipe open at both ends; length = 1 m Wave C: second harmonic; pipe open at both ends; length = 3 m Wave D: third harmonic; pipe closed at one end; length = 3 m

A $0.323-\mathrm{kg}$ clothesline is stretched with a tension of $53.4 \mathrm{~N}$ between two poles $6.10 \mathrm{~m}$ apart. What is the frequency of (a) the fundamental and (b) the second harmonic? (c) If the tension in the clothesline is increased, do the frequencies in parts (a) and (b) increase, decrease, or stay the same? Explain.

At point $A, 3.0$ m from a small source of sound that is emitting uniformly in all directions, the sound intensity level is $53 \mathrm{~dB}$.
(d) Does intensity obey the inverse-square law? What about sound intensity level?