The windpipe of one typical whooping crane is 5.00 feet long. What is the fundamental resonant frequency of the bird’s trachea, modeled as a narrow pipe closed at one end? Assume a temperature of 37$^ { \circ } \mathrm { C }$.

The A string on a cello vibrates in its first normal mode with a frequency of 220 Hz. The vibrating segment is 70.0 cm long and has a mass of 1.20 g. (a) Find the tension in the string. (b) Determine the frequency of vibration when the string vibrates in three segments.

A string with a mass m = 8.00 g and a length L = 5.00 m has one end attached to a wall; the other end is draped over a small, fixed pulley a distance d = 4.00 m from the wall and attached to a hanging object with a mass M = 4.00 kg. If the horizontal part of the string is plucked, what is the fundamental frequency of its vibration?

A string of length $L$, mass per unit length $\mu$, and tension $T$ is vibrating at its fundamental frequency. What effect will the following have on the fundamental frequency? (a) The length of the string is doubled, with all other factors held constant. (b) The mass per unit length is doubled, with all other factors held constant. (c) The tension is doubled, with all other factors held constant.

A sphere of mass M = 1.00 kg is supported by a string that passes over a pulley at the end of a horizontal rod of length L = 0.300 m. The string makes an angle $\theta=35.0^{\circ}$ with the rod. The fundamental frequency of standing waves in the portion of the string above the rod is f = 60.0 Hz. Find the mass of the portion of the string above the rod.

We know that an earthquake can produce a seiche in a lake in which the water sloshes back and forth from end to end with remarkably large amplitude and long periods. Consider a seiche produced in a rectangular farm pond. Suppose the pond is $9.15 \mathrm{~m}$ long and of uniform width and depth. You measure that a pulse produced at one end reaches the other end in $2.50 \mathrm{~s}$. To produce the seiche, several people stand on the bank at one end and paddle together with snow shovels, moving them in simple harmonic motion. What should be the frequency of this motion?

A string that is $30.0 \mathrm{~cm}$ long and has a mass per unit length of $9.00 \times 10^{-3} \mathrm{~kg} / \mathrm{m}$ is stretched to a tension of $20.0 \mathrm{~N}$. Find
(a) the fundamental frequency

A violin string has a length of 0.350 m and is tuned to concert G, with fG = 392 Hz. (a) How far from the end of the string must the violinist place her finger to play concert A, with fA = 440 Hz? (b) If this position is to remain correct to one-half the width of a finger (that is, to within 0.600 cm), what is the maximum allowable percentage change in the string tension?

A string is 0.400 m long and has a mass per unit length of $9.00 \times 10 - 3$ kg/m. What must be the tension in the string if its second harmonic has the same frequency as the second resonance mode of a 1.75-m-long pipe open at one end?

A tuning fork generates sound waves with a frequency of 246 Hz. The waves travel in opposite directions along a hallway, are reflected by end walls, and return. The hallway is 47.0 m long and the tuning fork is located 14.0 m from one end. What is the phase difference between the reflected waves when they meet at the tuning fork? The speed of sound in air is 343 m/s.

Two waves on one string are described by the wave functionsy1 = 3.0 cos (4.0x − 1.6t) y2 = 4.0 sin (5.0x − 2.0t)where x and y are in centimeters and t is in seconds. Find the superposition of the waves y1 + y2 at the points (a) x = 1.00, t = 1.00; (b) x = 1.00, t = 0.500; and (c) x = 0.500, t = 0 Note: Remember that the arguments of the trigonometric functions are in radians.

A taut string has a length of 2.60 m and is fixed at both ends. (a) Find the wavelength of the fundamental mode of vibration of the string. (b) Can you find the frequency of this mode? Explain why or why not.

A standing wave is established in a 120-cm-long string fixed at both ends. The string vibrates in four segments when driven at 120 Hz. (a) Determine the wavelength. (b) What is the fundamental frequency of the string?

Find the inverse function of the function f given by the set of ordered pairs. {(6, -2), (5, -3), (4, -4), (3, -5)}