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

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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 $v=3000\phantom{\rule{0.2em}{0ex}}\text{m/s?}$

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

can i get application of projectile motion?
when firing a cannon
morteza
Ok i got a question I'm not asking how gravity works. I would like to know why gravity works. like why is gravity the way it is. What is the true nature of gravity?
gravity pulls towards a mass...like every object is pulled towards earth
Ashok
One answer for that is exchange particles. Those particlescreate a field and if there is a field e.g. electromagnetic there is also force. same should go for gravitational field where exchange particle is called graviton and it creates gravitational field, which acts on everything that has mass.
Resid
@Ashok no that's how gravity works not why it works
Daniel
An automobile traveling with an initial velocity of 25m/s is accelerated to 35m/s in 6s,the wheel of the automobile is 80cm in diameter. find * The angular acceleration
what is the formula for pressure?
force/area
Kidus
force is newtom
Kidus
and area is meter squared
Kidus
so in SI units pressure is N/m^2
Kidus
In customary United States units pressure is lb/in^2. pound per square inch
Kidus
who is Newton?
scientist
Jeevan
a scientist
Peter
that discovered law of motion
Peter
ok
John
but who is Isaac newton?
John
a postmodernist would say that he did not discover them, he made them up and they're not actually a reality in itself, but a mere construct by which we decided to observe the word around us
elo
how?
Qhoshe
Besides his work on universal gravitation (gravity), Newton developed the 3 laws of motion which form the basic principles of modern physics. His discovery of calculus led the way to more powerful methods of solving mathematical problems. His work in optics included the study of white light and
Daniel
and the color spectrum
Daniel
what is a scalar quantity
scalar: are quantity have numerical value
muslim
is that a better way in defining scalar quantity
Peter
thanks
muslim
quantity that has magnitude but no direction
Peter
upward force and downward force lift
upward force and downward force on lift
hi
Etini
hi
elo
hy
Xander
Hello
Jux_dob
hi
Peter
Helo
Tobi
Daniel
what's the answer? I can't get it
what is the question again?
Sallieu
What's this conversation?
Zareen
what is catenation? and give examples
sununu
How many kilometres in 1 mile
Nessy
1.609km in 1mile
Faqir
what's the si unit of impulse
The Newton second (N•s)
Ethan
what is the s. I unit of current
Amphere(A)
imam
thanks man
Roland
u r welcome
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
what is head to tail rule?
kinza
what is the guess theorem
viva question and answer on practical youngs modulus by streching
send me vvi que
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
what are two dimensional force?