Exam 21: Superpositions

Two strings of identical material and radius are stretched with the same tension with their ends fixed, but one string is 8.0 mm longer than the other. Waves on these strings propagate at 420 m/s. The fundamental frequency of the longer string is 528 Hz. What is the beat frequency when each string is vibrating at its fundamental frequency?

A string, 0.28 m long and vibrating in its third harmonic, excites an open pipe that is 0.82 m long into its second overtone resonance. The speed of sound in air is 345 m/s. The speed of transverse waves on the string is closest to

An air column, open at one end and closed at the other, is being designed so that its second lowest resonant frequency is 440 Hz. What should be the length of the column if the speed of sound in air is 340 m/s?

Two harmonic sound waves reach an observer simultaneously. The observer hears the sound intensity rise and fall with a time of 0.200 s between the maximum intensity and the succeeding minimum intensity. What is the difference in frequency of the two sound waves?

Light is incident normally from air onto a liquid film that is on a glass plate. The liquid film is 164 nm thick, and the liquid has index of refraction 1.60. The glass has index of refraction n = 1.50. Calculate the longest visible wavelength (as measured in air) of the light for which there will be totally destructive interference between the rays reflected from the top and bottom surfaces of the film. (Assume that the visible spectrum lies between 400 and 700 nm.)

The speed of sound in the air inside a 0.640-m long gas column is 340 m/s. What is the fundamental resonant frequency of this air column if it is (a) open at one end and closed at the other end? (b) open at both ends?

Two optically flat glass plates, 16.0 cm long, are in contact at one end and separated by 0.0200 mm at the other end. The space between the plates is occupied by oil with index of refraction 1.45. The index of refraction of the glass plates is 1.55. The plates are illuminated at normal incidence with monochromatic light, and fringes are observed. If the dark fringes are spaced 2.00 mm apart, what is the wavelength of the monochromatic light?

A thin taut string is fixed at both ends and stretched along the horizontal x-axis with its left end at x = 0. It is vibrating in its third OVERTONE, and the equation for the vertical displacement of any point on the string is y(x,t) = (1.22 cm) sin[(14.4 m^-1)x] cos[(166 rad/s)t]. (a) What are the frequency and wavelength of the fundamental mode of this string? (b) How long is the string? (c) How fast do waves travel on this string?

Two pure tones are sounded together and a particular beat frequency is heard. What happens to the beat frequency if the frequency of one of the tones is increased?

A heavy stone of mass m is hung from the ceiling by a thin 8.25-g wire that is 65.0 cm long. When you gently pluck the upper end of the wire, a pulse travels down the wire and returns 7.84 ms later, having reflected off the lower end. The speed of sound in the room is 344 m/s, and the stone is heavy enough to prevent the lower end of the wire from moving. If the wire is vibrating in its second overtone, what is the frequency of the sound it will produce?

An organ pipe open at both ends has two successive harmonics with frequencies of 210 Hz and 240 Hz. What is the length of the pipe? The speed of sound is 344 m/s in air.

Consider the waves on a vibrating guitar string and the sound waves the guitar produces in the surrounding air. The string waves and the sound waves must have the same

A platinum wire that is 1.20 m long has a radius of 0.500 mm and is fixed at both ends. In its third harmonic it vibrates at 512 Hz. The density of platinum is 21.4 × 10³ kg/m³. What is the tension in the wire?

A thin layer of oil (n = 1.25) is on top of a puddle of water (n = 1.33). If normally incident 500-nm light is strongly reflected, what is the minimum nonzero thickness of the oil layer?

A 1.0-g string that is 0.64 m long is fixed at both ends and is under tension. This string produces a 100-Hz tone when it vibrates in the third harmonic. The speed of sound in air is 344 m/s. The tension in the string, in is closest to

Two violinists are trying to tune their instruments in an orchestra. One is producing the desired frequency of 440.0 Hz. The other is producing a frequency of 448.4 Hz. By what percentage should the out-of-tune musician change the tension in his string to bring his instrument into tune at 440.0 Hz?

A person is hearing two sound waves simultaneously. One has a period of 1.50 ms and the other one a period of 1.54 ms. What is the period of the beat due to these two waves?

The lowest-pitch tone to resonate in a pipe of length L that is open at both ends is 200 Hz. Which one of the following frequencies will NOT resonate in the same pipe?

A standing wave is oscillating at 690 Hz on a string, as shown in the figure. What is the speed of traveling waves on this string?

The tension in each of two strings is adjusted so that both vibrate at exactly 666 Hz. The tension in one of the strings is then increased slightly. As a result, six beats per second are heard when both strings vibrate. What is the new frequency of the string that was tightened?