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Why do roofs of gymnasiums and churches seem to fail more than family homes when an earthquake occurs?

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Wine glasses can be set into resonance by moistening your finger and rubbing it around the rim of the glass. Why?

Energy is supplied to the glass by the work done by the force of your finger on the glass. When supplied at the right frequency, standing waves form. The glass resonates and the vibrations produce sound.

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Air conditioning units are sometimes placed on the roof of homes in the city. Occasionally, the air conditioners cause an undesirable hum throughout the upper floors of the homes. Why does this happen? What can be done to reduce the hum?

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Consider a standing wave modeled as y ( x , t ) = 4.00 cm sin ( 3 m −1 x ) cos ( 4 s −1 t ) . Is there a node or an antinode at x = 0.00 m ? What about a standing wave modeled as y ( x , t ) = 4.00 cm sin ( 3 m −1 x + π 2 ) cos ( 4 s −1 t ) ? Is there a node or an antinode at the x = 0.00 m position?

For the equation y ( x , t ) = 4.00 cm sin ( 3 m −1 x ) cos ( 4 s −1 t ) , there is a node because when x = 0.00 m , sin ( 3 m −1 ( 0.00 m ) ) = 0.00 , so y ( 0.00 m , t ) = 0.00 m for all time. For the equation y ( x , t ) = 4.00 cm sin ( 3 m −1 x + π 2 ) cos ( 4 s −1 t ) , there is an antinode because when x = 0.00 m , sin ( 3 m −1 ( 0.00 m ) + π 2 ) = + 1.00 , so y ( 0.00 m , t ) oscillates between + A and − A as the cosine term oscillates between +1 and -1.

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Problems

A wave traveling on a Slinky® that is stretched to 4 m takes 2.4 s to travel the length of the Slinky and back again. (a) What is the speed of the wave? (b) Using the same Slinky stretched to the same length, a standing wave is created which consists of three antinodes and four nodes. At what frequency must the Slinky be oscillating?

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A 2-m long string is stretched between two supports with a tension that produces a wave speed equal to v w = 50.00 m/s . What are the wavelength and frequency of the first three modes that resonate on the string?

λ n = 2.00 n L , f n = v λ n λ 1 = 4.00 m , f 1 = 12.5 Hz λ 2 = 2.00 m , f 2 = 25.00 Hz λ 3 = 1.33 m , f 3 = 37.59 Hz

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Consider the experimental setup shown below. The length of the string between the string vibrator and the pulley is L = 1.00 m . The linear density of the string is μ = 0.006 kg/m . The string vibrator can oscillate at any frequency. The hanging mass is 2.00 kg. (a)What are the wavelength and frequency of n = 6 mode? (b) The string oscillates the air around the string. What is the wavelength of the sound if the speed of the sound is v s = 343.00 m/s?

A string vibrator is shown on the left of the figure. A string is attached to its right. This goes over a pulley and down the side of the table. A hanging mass m is suspended from it. The pulley is frictionless. The distance between the pulley and the string vibrator is L. It is labeled mu equal to dm by dx equal to constant.
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A cable with a linear density of μ = 0.2 kg/m is hung from telephone poles. The tension in the cable is 500.00 N. The distance between poles is 20 meters. The wind blows across the line, causing the cable resonate. A standing waves pattern is produced that has 4.5 wavelengths between the two poles. The air temperature is T = 20 ° C . What are the frequency and wavelength of the hum?

v = 158.11 m/s, λ = 4.44 m, f = 35.61 Hz λ s = 9.63 m

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Consider a rod of length L , mounted in the center to a support. A node must exist where the rod is mounted on a support, as shown below. Draw the first two normal modes of the rod as it is driven into resonance. Label the wavelength and the frequency required to drive the rod into resonance.

Figure shows a horizontal rod of length L = 2 m supported at the centre by a pole.
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Consider two wave functions y ( x , t ) = 0.30 cm sin ( 3 m −1 x 4 s −1 t ) and y ( x , t ) = 0.30 cm sin ( 3 m −1 x + 4 s −1 t ) . Write a wave function for the resulting standing wave.

y ( x , t ) = [ 0.60 cm sin ( 3 m −1 x ) ] cos ( 4 s −1 t )

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Questions & Answers

number of lines passing through area which is placed at some angle. these line are are produced by charge(+ or -).
M. Reply
hstjsbks
Junaid Reply
define electric flux? find the electric field due to a long strainght line
Aslam Reply
Clay Matthews, a linebacker for the Green Bay Packers, can reach a speed of 10.0 m/s. At the start of a play, Matthews runs downfield at 43° with respect to the 50-yard line (the +x-axis) and covers 7.8 m in 1 s. He then runs straight down the field at 90° with respect to the 50-yard line (that is, in the +y-direction) for 17 m, with an elapsed time of 2.9 s. (Express your answers in vector form.) (a) What is Matthews's final displacement (in m) from the start of the play?
Justin Reply
What is his average velocity (in m/s)?
Justin
A machine at a post office sends packages out a chute and down a ramp to be loaded into delivery vehicles. (a) Calculate the acceleration of a box heading down a 17.4° slope, assuming the coefficient of friction for a parcel on waxed wood is 0.100. (b) Find the angle of the slope down which this box could move at a constant velocity. You can neglect air resistance in both parts.
Austin Reply
what principle is applicable in projectile motion
Mkapa Reply
does rocket and satellite follow the same principle??? which principle do both of these follow???
Abhishek Reply
According to d'Broglie's concept of matter waves matter behaves like wave and the wavelength is h/p. but actually there is not only a wave but a wave packet wich is defined by a wave function and that wave function can defines everything about the particle but restricted by the uncertainty principle
Ravi Reply
what phenomenon describes Matter behave as a wave???
SHAKIRU Reply
simple definition of wave
Prajwal Reply
hello
Carls Reply
can anyone help me with this problem
Carls
A projectile is shot at a hill, the base of which is 300 m away. The projectile is shot at 60°60° above the horizontal with an initial speed of 75 m/s. The hill can be approximated by a plane sloped at 20°20° to the horizontal. Relative to the coordinate system shown in the following figure, the equation of this straight line is y=(tan20°)x−109.y=(tan20°)x−109. Where on the hill does the projectile land?
Carls
what is velocity
Abel Reply
hi, Musa,this moment a lateral
Arzoodan Reply
what is moment
Musa Reply
about projectile
Indra Reply
Practice Key Terms 6

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Source:  OpenStax, University physics volume 1. OpenStax CNX. Sep 19, 2016 Download for free at http://cnx.org/content/col12031/1.5
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