Example 18.1 Two Speakers Driven by the Same Sourcephysics.skku.ac.kr/xe/general_physics_study/Ch18/... · 2017. 3. 21. · Example 18.1 Two Speakers Driven by the Same Source Two

Example 18.1 Two Speakers Driven by the Same SourceTwo identical loudspeakers placed 3.00 m apart are driven by the same oscillator. A listener is originally at point O, located 8.00 m from the center of the line connecting the two speakers. The listener then moves to point P, which is a perpendicular distance 0.350 m from O, and she experiences the first minimum in sound intensity. What is the frequency of the oscillator?

Example 18.2 Formation of a Standing WaveTwo waves traveling in opposite directions produce a standing wave. The individual wave functions are

y1 = 4.0 sin (3.0 x – 2.0 t)y2 = 4.0 sin (3.0 x + 2.0 t)

where x and y are measured in centimeters and t is in seconds.

(A) Find the amplitude of the simple harmonic motion of the element of the medium located at x = 2.3 cm.

(B) Find the positions of the nodes and antinodes if one end of the string is at x = 0.

Example 18.3 Give Me a C Note!The middle C string on a piano has a fundamental frequency of 262 Hz, and thestring for the first A above middle C has a fundamental frequency of 440 Hz.

(A) Calculate the frequencies of the next two harmonics of the C string.

(B) If the A and C strings have the same linear mass density μ and length L, determine the ratio of tensions in the two strings.

Example 18.4 Changing String Vibration with WaterOne end of a horizontal string is attached to a vibrating blade, and the other endpasses over a pulley. A sphere of mass 2.00 kg hangs on the end of the string. The string is vibrating in its second harmonic. A container of water is raised under the sphere so that the sphere is completely submerged. In this configuration, the string vibrates in its fifth harmonic.What is the radius of the sphere?

Example 18.5 Wind in a CulvertA section of drainage culvert 1.23 m in length makes a howling noise when the wind blows across its open ends.

(A) Determine the frequencies of the first three harmonics of the culvert if it is cylindrical in shape and open at both ends. Take v = 343 m/s as the speed of sound in air.

(B) What are the three lowest natural frequencies of the culvert if it is blocked at one end?

Example 18.6 Measuring the Frequency of a Tuning ForkA simple apparatus for demonstrating resonance in an air column. A vertical pipe open at both ends is partially submerged in water, and a tuning fork vibrating at an unknown frequency is placed near the top of the pipe. The lengthL of the air column can be adjusted by moving the pipe vertically. The sound waves generated by the fork are reinforced when L corresponds to one of the resonance frequencies of the pipe. For a certain pipe, the smallest value of L forwhich a peak occurs in the sound intensity is 9.00 cm.

(A) What is the frequency of thetuning fork?

(B) What are the values of L for thenext two resonance conditions?

Example 18.7 The Mistuned Piano StringsTwo identical piano strings of length 0.750 m are each tuned exactly to 440 Hz. The tension in one of the strings is then increased by 1.0%. If they are now struck, what is the beat frequency between the fundamentals of the two strings?