# 16.6 Standing waves and resonance  (Page 7/17)

 Page 8 / 17

A 2.40-m wire has a mass of 7.50 g and is under a tension of 160 N. The wire is held rigidly at both ends and set into oscillation. (a) What is the speed of waves on the wire? The string is driven into resonance by a frequency that produces a standing wave with a wavelength equal to 1.20 m. (b) What is the frequency used to drive the string into resonance?

A string with a linear mass density of 0.0062 kg/m and a length of 3.00 m is set into the $n=100$ mode of resonance. The tension in the string is 20.00 N. What is the wavelength and frequency of the wave?

$\begin{array}{}\\ \\ {\lambda }_{100}=0.06\phantom{\rule{0.2em}{0ex}}\text{m}\hfill \\ \\ v=56.8\phantom{\rule{0.2em}{0ex}}\text{m/s,}\phantom{\rule{1em}{0ex}}{f}_{n}=n{f}_{1},\phantom{\rule{1em}{0ex}}n=1,2,3,4,5\text{...}\hfill \\ {f}_{100}=947\phantom{\rule{0.2em}{0ex}}\text{Hz}\hfill \end{array}$

A string with a linear mass density of 0.0075 kg/m and a length of 6.00 m is set into the $n=4$ mode of resonance by driving with a frequency of 100.00 Hz. What is the tension in the string?

Two sinusoidal waves with identical wavelengths and amplitudes travel in opposite directions along a string producing a standing wave. The linear mass density of the string is $\mu =0.075\phantom{\rule{0.2em}{0ex}}\text{kg/m}$ and the tension in the string is ${F}_{T}=5.00\phantom{\rule{0.2em}{0ex}}\text{N}.$ The time interval between instances of total destructive interference is $\text{Δ}t=0.13\phantom{\rule{0.2em}{0ex}}\text{s}.$ What is the wavelength of the waves?

$T=2\text{Δ}t,\phantom{\rule{1em}{0ex}}v=\frac{\lambda }{T},\phantom{\rule{1em}{0ex}}\lambda =2.12\phantom{\rule{0.2em}{0ex}}\text{m}$

A string, fixed on both ends, is 5.00 m long and has a mass of 0.15 kg. The tension if the string is 90 N. The string is vibrating to produce a standing wave at the fundamental frequency of the string. (a) What is the speed of the waves on the string? (b) What is the wavelength of the standing wave produced? (c) What is the period of the standing wave?

A string is fixed at both end. The mass of the string is 0.0090 kg and the length is 3.00 m. The string is under a tension of 200.00 N. The string is driven by a variable frequency source to produce standing waves on the string. Find the wavelengths and frequency of the first four modes of standing waves.

$\begin{array}{}\\ \\ {\lambda }_{1}=6.00\phantom{\rule{0.2em}{0ex}}\text{m},\phantom{\rule{1em}{0ex}}{\lambda }_{2}=3.00\phantom{\rule{0.2em}{0ex}}\text{m},\phantom{\rule{1em}{0ex}}{\lambda }_{3}=2.00\phantom{\rule{0.2em}{0ex}}\text{m},\phantom{\rule{1em}{0ex}}{\lambda }_{4}=1.50\phantom{\rule{0.2em}{0ex}}\text{m}\hfill \\ v=258.20\phantom{\rule{0.2em}{0ex}}\text{m/s}=\lambda f\hfill \\ {f}_{1}=43.03\phantom{\rule{0.2em}{0ex}}\text{Hz},\phantom{\rule{1em}{0ex}}{f}_{2}=86.07\phantom{\rule{0.2em}{0ex}}\text{Hz},\phantom{\rule{1em}{0ex}}{f}_{3}=129.10\phantom{\rule{0.2em}{0ex}}\text{Hz},\phantom{\rule{1em}{0ex}}{f}_{4}=172.13\phantom{\rule{0.2em}{0ex}}\text{Hz}\hfill \end{array}$

The frequencies of two successive modes of standing waves on a string are 258.36 Hz and 301.42 Hz. What is the next frequency above 100.00 Hz that would produce a standing wave?

A string is fixed at both ends to supports 3.50 m apart and has a linear mass density of $\mu =0.005\phantom{\rule{0.2em}{0ex}}\text{kg/m}.$ The string is under a tension of 90.00 N. A standing wave is produced on the string with six nodes and five antinodes. What are the wave speed, wavelength, frequency, and period of the standing wave?

$v=134.16\phantom{\rule{0.2em}{0ex}}\text{ms},\lambda =1.4\phantom{\rule{0.2em}{0ex}}\text{m},f=95.83\phantom{\rule{0.2em}{0ex}}\text{Hz},T=0.0104\phantom{\rule{0.2em}{0ex}}\text{s}$

Sine waves are sent down a 1.5-m-long string fixed at both ends. The waves reflect back in the opposite direction. The amplitude of the wave is 4.00 cm. The propagation velocity of the waves is 175 m/s. The $n=6$ resonance mode of the string is produced. Write an equation for the resulting standing wave.

Ultrasound equipment used in the medical profession uses sound waves of a frequency above the range of human hearing. If the frequency of the sound produced by the ultrasound machine is $f=30\phantom{\rule{0.2em}{0ex}}\text{kHz,}$ what is the wavelength of the ultrasound in bone, if the speed of sound in bone is $v=3000\phantom{\rule{0.2em}{0ex}}\text{m/s?}$

$\lambda =0.10\phantom{\rule{0.2em}{0ex}}\text{m}$

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1 mile * 1609m
Boon
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i wanted to know the steps
Shrushti
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Rashid
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Asutosh
Olympus Mons on Mars is the largest volcano in the solar system, at a height of 25 km and with a radius of 312 km. If you are standing on the summit, with what initial velocity would you have to fire a projectile from a cannon horizontally to clear the volcano and land on the surface of Mars? Note that Mars has an acceleration of gravity of 3.7 m/s2 .
what is summit
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Ngeh
पृथवी को इसके अक्ष पर कितने कोणीय चाल से घूमाऐ कि भूमधय पे आदमी का भार इसके वासतविक भार से 3/5अधिक हो
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Murari
At a post office, a parcel that is a 20.0-kg box slides down a ramp inclined at 30.0° 30.0° with the horizontal. The coefficient of kinetic friction between the box and plane is 0.0300. (a) Find the acceleration of the box. (b) Find the velocity of the box as it reaches the end of the plane, if the length of the plane is 2 m and the box starts at rest.
As an IT student must I take physics seriously?
yh
Bernice
hii
Raja
IT came from physics and maths so I don't see why you wouldn't
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that is a question you can find on Google, anyway of top of my head, compass, ruler, protractor, try square, triangles.
Rongfang
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2F
Jacob
it will be doubled
kelvin
double
Devesh
The difference between vector and scaler quantity
vector has both magnitude & direction but scalar has only magnitude
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ron
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Inusah
use the socatoa rule
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draw force diagram, then work out the direction of force.
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explain what Newtonian mechanics is.
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Arzoodan
what is the meaning of single term,mechanics?
jyotirmayee
mechanics is the science related to the behavior of physical bodies when some external force is applied to them
Lalita
SO ASK What is Newtonian mechanics in physics? Newtonian physics, also calledNewtonian or classical mechanics, is the description of mechanical events—those that involve forces acting on matter—using the laws of motion and gravitation formulated in the late seventeenth century by English physicist
Suleiman
can any one send me the best reference book for physics?
Prema
concept of physics by HC verma, Fundamentals of Physics, university of physics
tq u.
Prema
these are the best physics books one can fond both theory and applications.
can any one suggest best book for maths with lot of Tricks?
Vivek
what is the water height in barometer?
SUNEELL
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LOVE
water is 13.5 times dense than the Mercury
LOVE
plz tell me frnds the best reference book for physics along with the names of authors.
Prema
i recomended the reference book for physics from library University of Dublin or library Trinity college
Arzoodan
A little help here... . 1. Newton's laws of Motion, are they applicable to motions of all speeds? 2.state the speeds which are applicable to Newtons laws of Motion
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jyotirmayee
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jyotirmayee
prove Newton's first law of motion
prince
Hello frnds what is physics in general?
Ngeh
A block of mass m is attached to a spring with spring constant k and free to slide along a horizontal frictionless surface. At t=0, the block spring system is stretched on amount x>0 from the equilibrium position and is released from rest Vx = 0 What is the period of oscillation of the block? What
Ella
What is the velocity of the block when it first comes back to the equilibrium position?
Ella