Chapter+13,14+waves

Composed by the Miraculous, Fabled, Unfathomably-Mysterious Matthew D. Easton

__**Chapter 13**__

Spring Constant: stiffness of a spring Audible Waves: longitudinal waves that lie within the range of sensitivity of the ear Infrasonic Waves: waves whose frequencies are below the range of the ears Ultrasonic Waves: waves whose frequencies are above the range of the ears Threshold of Pain: ~1 W/m^2 Mach Number: Ratio of speed of object to speed of sound Mechanical Wave: a disturbance transmitted by a medium from one point to another without the medium itself being transported Crest: point of maximum vertical displacement above horizontal of a wave Trough: point of maximum vertical displacement under horizontal of a wave Wavelength: distance between two adjacent crests or troughs Amplitude: maximum displacement from horizontal equilibrium along a wave (trough to equilibrium or crest to equilibrium, NOT distance from trough to crest) Transverse wave: oscillation which is characterized by motion of the wave perpendicular to the direction wave is traveling Period: time to complete one cycle or oscillation Frequency: number of cycles or oscillations per second Superposition: algebraic sum of displacements of two individual waves traveling along same medium Constructive Interference: combined wave that has a greater magnitude than either individual wave Destructive Interference: combined wave that has a smaller magnitude than either individual wave In Phase: crests and troughs meet at same points Out of Phase: crest meets trough, trough meets crest Standing Wave: wave reflected back off of a surface (e.g. wall) with fixed oscillation Node: points alone standing wave where no motion occurs Antinodes: points along standing wave where maximum motion occurs Harmonic (Resonant) Wavelengths: equally-spaced wavelengths across standing wave (double the length divided by harmonic number) Harmonic (Resonant) Frequencies: equally-timed frequencies across standing wave (harmonic number times velocity divided by double the length Fundamental Standing Wave: standing wave where harmonic number is 1 Longitudinal Wave: motion of molecules in the medium is parallel to the direction of the wave Intensity: energy per unity area Decibels: loudness of sound (dB) Doppler Effect: shift in frequency that occurs when the source and detector are in relative motion
 * Vocabulary-**


 * Equations-**



1. A 12 cm-long spring has a force constant k of 400 N/m. How much force is required to stretch the spring to a length of 14 cm?
 * Example Problems-**
 * F=kx, thus (400 N/m)(.02 m) = 8 N

2. A block of mass m=.05 kg oscillates on a spring whose force constant k is 500 N/m. The amplitude of the oscillations is 4.0 cm. What is the maximum speed?
 * Maximum elastic potential energy, thus .5kA^2=.5mv^2 = 4 m/s

3. A block of mass m=8.0 kg is attached to an ideal spring of force constant k=500 N/m. The block is at rest at its equilibrium position. An impulsie force acts on the block, giving it an initial speed of 2.0 m/s. Find the amplitude of the resulting oscillations.
 * The block will come to rest when all of its initial kinetic energy has been transformed into the spring's potential energy, thus .5mv^2 = .5kA^2 = .25 m

4. A student observing an oscillating block counts 45.5 cylces of oscillation in one minute. Determine its frequency (in Hertz) and period (in seconds).
 * Frequency must be in terms of cycles per second, thus cycles/minute * minute/second = .758 Hz
 * Period is one divided by the frequency, thus 1/frequency = 1.32 seconds

5. A block is attached to a spring and set into oscillatory motion, and its frequency is measured. If this block were removed and replaced by a second block with 1/4 the mass of the first block, how would the frequency of the oscillations compare to that of the first block?
 * Frequency is inversely proportional to the square root of the mass of the block, thus 1/m^.5 = 2

6. A block of mass m=1.5 kg is attached to the end of a vertical spring of force constant k=300 N/m. After the block comes to rest, it is pulled down a distance of 2.0 cm and released. (a) What is the frequency of the resulting oscillations? (b) What are the minimum and maximum amounts of stretch of the spring during the oscillations of the block?
 * Frequency can be described as the square root of k divided by m, multiplied by one over two pi = 2.3 Hz
 * d=mg/k = 5 cm

7. The period of a traveling wave is .5 s, its amplitude is 10 cm, and its wavelength is .4 m. What are its frequency and wave speed?
 * Frequency is one over period, thus = 2 Hz
 * Wave speed is wavelength times frequency, thus = 0.6 m

8. Write the equation for a transverse wave traveling in the +x direction with a frequency of 6 Hz, wavelength of 0.2 m, amplitude 8 cm, given that the left end of the rope has zero displacement at time t=0.
 * y=0.08sin[2pi(6t-5x0]

9. A string of length 10 m and mass 300 g is fixed at both ends, and the tension in the string is 40 N. What is the frequency of the standing wave for which the distance between a node and the closest antinode is 1 m?
 * Wavelength equals 2L/n, thus n = 5
 * Find the frequency at the fifth harmonic means using equation F = (nv)/2L with Equation #10 (from above on this page) = 9.1 Hz

10. A sound wave traveling through water has a frequency of 500 Hz and a wavelength of 3 m. How fast does sound travel through water?
 * Velocity is wavelength times frequency, thus = 1500 m/s

11. A source of 4 kHz sound waves travels at 1/9 the speed of sound toward a detector that's moving at 1/9 the speed of sound toward the source. (a) What is the frequency of the waves as they're received by the detector? (b) How does the wavelength of the detected waves compare to the wavelength of the emitted waves?
 * Using Doppler Effect equation (F = (V+Vo)/(V+Vs)), = 5 kHz
 * Wavelength will shift down by inverse of factor, thus 4/5

1. Which of the following is/are characteristics of simple harmonic motion? I. The acceleration is constant II. The restoring force is proportional to the displacement III. The frequency is independent of the amplitude
 * Multiple Choice Questions-**

A) II only B) I and II only C) I and III only D) II and III only E) I, II, and III

2. A student measures the maximum speed of a block undergoing simple harmonic oscillation of amplitude A on the end of an ideal spring. If the block is replaced by one with twice the mass but the amplitude of its oscillation remains the same, then the maximum speed of the block will

A) decrease by a factor of 4 B) decrease by a factor of 2 C) decrease by a factor of the square root of 2 D) remain the same E) increase by a factor of two

3. The vertical displacement, y, of a transverse traveling wave is given by the equation y=6sin(10t(pi)-.5x(pi)), with x and y in centimeters and t in seconds. What is the wavelength?

A) .25 cm B) .5 cm C) 2 cm D) 4 cm E) 8 cm

4. A block attached to an ideal spring undergoes simple harmonic motion about its equilibrium position (x=0) with amplitude A. What fraction of the total energy is in the form of kinetic energy when the block is at position x=.5A?

A) 1/3 B) 3/8 C) 1/2 D) 2/3 E) 3/4

5. A string, fixed at both ends, has a length of 6 m and supports a standing wave with a total of 4 nodes. If a transverse wave can travel at 40 m/s down the rope, what is the frequency of this standing wave?

A) 6.7 Hz B) 10 Hz C) 13.3 Hz D) 20 Hz E) 26.7 Hz

6. An observer is 2 m from a source of sound waves. By how much will the sound level decrease if the observer moves to a distance of 20 m?

A) 1 dB B) 2 dB C) 10 dB D) 18 dB E) 20 dB

7. An organ pipe that's closed at one end has a length of 17 cm. If the speed of sound through the air inside is 340 m/s, what is the pipe's fundamental frequency?

A) 250 Hz B) 500 Hz C) 1000 Hz D) 1500 Hz E) 2000 Hz

8. A simple pendulum swings about the vertical equilibrium position with a maximum angular displacement of 5 degrees and period T. If the same pendulum is given a maximum angular displacement of 10 degrees, then which of the following best gives the period of the oscillations?

A) T/2 B) T/(2^.5) C) T D) T(2^.5) E) 2T


 * Videos-**

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