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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

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Rachel Reply
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Sallieu
What's this conversation?
Zareen
what is catenation? and give examples
sununu
what's the si unit of impulse
Iguh Reply
The Newton second (N•s)
Ethan
what is the s. I unit of current
Roland Reply
Amphere(A)
imam
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Roland
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imam
the velocity of a boat related to water is 3i+4j and that of water related to earth is i-3j. what is the velocity of the boat relative to earth.If unit vector i and j represent 1km/hour east and north respectively
Pallavi Reply
what is head to tail rule?
kinza Reply
Explain Head to tail rule?
kinza
what is the guess theorem
Monu Reply
viva question and answer on practical youngs modulus by streching
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rupesh
a car can cover a distance of 522km on 36 Liter's of petrol, how far can it travel on 14 liter of petrol.
Isaac
yoo the ans is 193
Joseph
whats a two dimensional force
Jimoh Reply
what are two dimensional force?
Ahmad
Where is Fourier Theorem?
Atul Reply
what is Boyle's law
Amoo Reply
Boyle's law state that the volume of a given mass of gas is inversely proportion to its pressure provided that temperature remains constant
Abe
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Huntergirl
what is the meaning of in.
CHUKWUMA Reply
In means natural logarithm
Elom
is dea graph for cancer caliper experiment using glass block?
Bako
identity of vectors?
Choudhry Reply
what is defined as triple temperature
Prince Reply
Triple temperature is the temperature at which melting ice and boiling water are at equilibrium
njumo
a tire 0.5m in radius rotate at constant rate 200rev/min. find speed and acceleration of small lodged in tread of tire.
Tahira Reply
hmm
Ishaq
100
Noor
define the terms as used in gravitational mortion 1:earth' satellites and write two example 2:parking orbit 3:gravitation potential 4:gravitation potential energy 5:escping velocity 6:gravitation field and gravitation field strength
Malima Reply
can gravitational force cause heat?
SANT
yes
Kawshik
_2/3 ÷34
Isaac
does gravitation affect friction
Joseph
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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