Exam 14: Periodic Motion

Mathematics of traveling waves: Four traveling waves are described by the following equations, where all quantities are measured in SI units and y represents the displacement. I: y = 0.12 cos(3x + 2t) II: y = 0.15 sin(6x - 3t) III: y = 0.23 cos(3x + 6t) IV: y = -0.29 sin(1.5x - t) Which of these waves have the same speed?

Doppler effect: A carousel that is 5.00 m in radius has a pair of 600-Hz sirens mounted on posts at opposite ends of a diameter. The carousel rotates with an angular velocity of 0.800 rad/s. A stationary listener is located at a distance from the carousel. The speed of sound is 350 m/s. The longest wavelength reaching the listener from the sirens is closest to

Sound level: A certain source of sound waves radiates uniformly in all directions. At a distance of 20 m from the source the intensity level is 51 db. What is the total acoustic power output of the source, in watts? (Note: The reference intensity I₀ is 1.0 × 10^-12 W/m².)

Standing sound waves: The lowest-pitch tone to resonate in a pipe of length L that is closed at one end and open at the other end is 200 Hz. Which one of the following frequencies will NOT resonate in the same pipe?

Intensity: Observer A is 3.0 m from a tiny light bulb and observer B is 12.0 m from the same bulb. Assume that the light spreads out uniformly and undergoes no significant reflections or absorption. If observer B sees a light of intensity I, the light intensity that A sees is

Standing sound waves: 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?

Sound level: The sound level at 1.0 m from a certain talking person talking is 60 dB. You are surrounded by five such people, all 1.0 m from you and all talking equally loud at the same time. The threshold of hearing is 1.0 × 10^-12 W/m². What sound level are you being exposed to? You can neglect any absorption, reflection, or interference of the sound. The threshold of hearing is 1.0 × 10^-12 W/m².

Intensity: A transverse wave traveling along a string transports energy at a rate r. If we want to double this rate, we could

Doppler effect: A factory siren indicating the end of a shift has a frequency of 90.0 Hz. The speed of sound is 343 m/s. (a) What frequency is perceived by the occupant of a car traveling towards the factory at 25.0 m/s? (b) What frequency is perceived by the occupant of a car traveling away from the factory at 30.0 m/s?

Sound level: Which one of the following statements is true?

Intensity: Two people are talking at a distance of 3.0 m from where you are and you measure the sound intensity as 1.1 × 10^-7 W/m². Another student is 4.0 m away from the talkers. What sound intensity does the other student measure? Assume that the sound spreads out uniformly and undergoes no significant reflections or absorption.

Standing sound waves: A 1.30-m long gas column that is open at one end and closed at the other end has a fundamental resonant frequency 80.0 Hz. What is the speed of sound in this gas?

Beats: Two motors in a factory are running at slightly different rates. One runs at 825 rpm and the other at 786 rpm. You hear the sound intensity increase and then decrease periodically due to wave interference. How much time elapses between successive maxima of the sound intensity?

Standing sound 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?

Mathematics of traveling waves: The figure shows the displacement y of a traveling wave at a given position as a function of time and the displacement of the same wave at a given time as a function of position. How fast is the wave traveling?

Shock waves: A supersonic plane passes overhead at a speed of 500 m/s. If you hear the sonic boom (shock wave) 4.00 s after the plane is directly overhead, at what altitude is the plane flying? Assume the speed of sound in air is 340 m/s.

Doppler effect: Two in-phase loudspeakers are some distance apart. They emit sound with a frequency of 1536 Hz. You move between the speakers, along the line joining them, at a constant speed of 2.8 m/s. What beat frequency do you observe? The speed of sound in the room is 330 m/s.

Standing sound waves: A pipe that is 120 cm long resonates to produce sound of wavelengths 480 cm, 160 cm, and 96 cm but does not resonate at any wavelengths longer than these. This pipe is

Sound: What characteristic of sound determines the "pitch" of a musical note?

Intensity: A tiny vibrating source sends waves uniformly in all directions. An area of 3.25 cm² on a sphere of radius 2.50 m centered on the source receives energy at a rate of 4.20 J/s. (a) What is the intensity of the waves at 2.50 m from the source and at 10.0 m from the source? (b) At what rate is energy leaving the vibrating source of the waves?