17.5 Sources of Musical Sound

Consider three pipes of the same length (L). Pipe A is open at both ends, pipe B is closed at both ends, and pipe C has one open end and one closed end. If the velocity of sound is the same in each of the three tubes, in which of the tubes could the lowest fundamental frequency be produced? In which of the tubes could the highest fundamental frequency be produced?

A string is tied between two lab posts a distance L apart. The tension in the string and the linear mass density is such that the speed of a wave on the string is $v = 343 \text{m}/\text{s} .$ A tube with symmetric boundary conditions has a length L and the speed of sound in the tube is $v = 343 \text{m}/\text{s} .$ What could be said about the frequencies of the harmonics in the string and the tube? What if the velocity in the string were $v = 686 \text{m}/\text{s}$?

What are the first three overtones of a bassoon that has a fundamental frequency of 90.0 Hz? It is open at both ends. (The overtones of a real bassoon are more complex than this example, because its double reed makes it act more like a tube closed at one end.)

What length should an oboe have to produce a fundamental frequency of 110 Hz on a day when the speed of sound is 343 m/s? It is open at both ends.

An organ pipe $\left(L = 3.00 \text{m}\right)$ is closed at both ends. Compute the wavelengths and frequencies of the first three modes of resonance. Assume the speed of sound is$v = 343.00 \text{m}/\text{s} .$

A sound wave of a frequency of 2.00 kHz is produced by a string oscillating in the $n = 6$ mode. The linear mass density of the string is $\mu = 0.0065 \text{kg}/\text{m}$ and the length of the string is 1.50 m. What is the tension in the string?

A student holds an 80.00-cm lab pole one quarter of the length from the end of the pole. The lab pole is made of aluminum. The student strikes the lab pole with a hammer. The pole resonates at the lowest possible frequency. What is that frequency?

By what fraction will the frequencies produced by a wind instrument change when air temperature goes from $10.0 ° \text{C}$ to $30.0 ° \text{C}$? That is, find the ratio of the frequencies at those temperatures.