1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
inessss [21]
3 years ago
14

(a) Write an equation describing a sinusoidal transverse wave traveling on a cord in the positive of a y axis with an angular wa

ve number of a period of 0.20 s, and an amplitude of 3.0 mm. Take the transverse direction to be the z direction.
(b) What is the maximum transverse speed of a point on the cord?
(c) What is the wave speed?
Physics
1 answer:
Vedmedyk [2.9K]3 years ago
7 0

Missing data: the wave number

k=60 cm^{-1}

(a)  z = 0.003 sin (6000y-31.4 t)

For a transverse wave travelling in the positive y-direction and with vibration along the z-direction, the equation of the wave is

z = A sin (ky-\omega t)

where

A is the amplitude of the wave

k is the wave number

\omega is the angular frequency

t is the time

In this situation:

A = 3.0 mm = 0.003 m is the amplitude

k = 60 cm^{-1} = 6000 m^{-1} is the wave number

T = 0.20 s is the period, so the angular frequency is

\omega=\frac{2\pi}{T}=\frac{2\pi}{0.20}=31.4 rad/s

So, the wave equation (in meters) is

z = 0.003 sin (6000y-31.4 t)

(b) 0.094 m/s

For a transverse wave, the transverse speed is equal to the derivative of the displacement of the wave, so in this case:

v_t = z' = -A \omega cos (ky-\omega t)

So the maximum transverse wave occurs when the cosine term is equal to 1, therefore the maximum transverse speed must be

v_{t}_{max} =\omega A

where

\omega = 31.4 rad/s\\A = 0.003 m

Substituting,

v_{t}_{max}=(31.4)(0.003)=0.094 m/s

(c) 5.24 mm/s

The wave speed is given by

v=f \lambda

where

f is the frequency of the wave

\lambda is the wavelength

The frequency can be found from the angular frequency:

f=\frac{\omega}{2\pi}=\frac{31.4}{2\pi}=5 Hz

While the wavelength can be found from the wave number:

\lambda = \frac{2\pi}{k}=\frac{2\pi}{6000}=1.05\cdot 10^{-3} m

Therefore, the wave speed is

v=(5)(1.05\cdot 10^{-3} )=5.24 \cdot 10^{-3} m/s = 5.24 mm/s

You might be interested in
If you wanted to discover the youngest stars you could find in some grouping of stars in the Galaxy, which type of star group wo
Vilka [71]

Answer:

Associations Clusters

Explanation:

There is three basic type of clusters, globular clusters, open clusters, associations clusters. Associations cluster consist of younger stars that is younger than globular and open clusters stars.

7 0
3 years ago
You are designing a 108 cm3 right circular cylindrical can whose manufacture will take waste into account. There is no waste in
FinnZ [79.3K]

Explanation:

It is given that,

The volume of a right circular cylindrical, V=108\ cm^3

We know that the volume of the cylinder is given by :

V=\pi r^2 h

108=\pi r^2 h    

h=\dfrac{108}{\pi r^2}............(1)

The upper area is given by :

A=32r^2+2\pi rh

A=32r^2+2\pi r\times \dfrac{108}{\pi r^2}

A=32r^2+\dfrac{216}{r}

For maximum area, differentiate above equation wrt r such that, we get :

\dfrac{dA}{dr}=64r-\dfrac{216}{r^2}

64r-\dfrac{216}{r^2}=0

r^3=\dfrac{216}{64}

r = 1.83 m

Dividing equation (1) with r such that,

\dfrac{h}{r}=\dfrac{108}{\pi r}

\dfrac{h}{r}=\dfrac{108}{\pi 1.83}

\dfrac{h}{r}=59 \pi

Hence, this is the required solution.

8 0
3 years ago
In a series lrc circuit, the frequency at which the circuit is at resonance is f0. If you double the resistance, the inductance,
taurus [48]

When you double capacitance and inductance, the new resonance frequency becomes f/2.

  • Resonance frequency:

The resonance frequency of RLC series circuit, is the frequency at which the capacity reactance is equal to inductive reactance.

It can also be defined as the natural frequency of an object where it tends to vibrate at a higher amplitude.

Xc = Xl

which gives the value for resonance frequency:

f = \frac{1}{2\pi \sqrt{LC} }

where;

f is the resonance frequency

L is the inductance

C is the capacitance

When you double capacitance and inductance, the new resonance frequency becomes;

f' = \frac{1}{2\pi \sqrt{2L2C} }

f' = \frac{1}{2\pi \sqrt{4LC} }

f' = \frac{1}{\pi \sqrt{LC} }\frac{1}{2}

f' = \frac{1}{2} f

Thus from above,

When you double capacitance and inductance, the new resonance frequency becomes f/2.

Learn more about resonance frequency here:

<u>brainly.com/question/13040523</u>

#SPJ4

6 0
2 years ago
For her birthday, amy received flowers that had a dull red appearance. compared with the entire range of visible light waves, th
Cerrena [4.2K]
The flowers reflect relatively low frequency and low amplitude light waves.
White light contains a spectrum of colors, and red light is at the beginning of this spectrum in terms of energy. This means that it has the lowest frequency, as the energy of a wave of light is directly proportional to its frequency.
The amplitude of a light wave gives a measure of how intense the light is. A dull light means that the amplitude of the wave is low.
4 0
3 years ago
Plz help it should be super easy
fgiga [73]

Answer:

yes it is easy

Explanation:

6 0
3 years ago
Read 2 more answers
Other questions:
  • Let at time t1 means?
    6·1 answer
  • Of waterfalls with a height of more than 50 m , Niagara Falls in Canada has the highest flow rate of any waterfall in the world.
    12·1 answer
  • Which layer of the Sun appears pinkish-red during a solar eclipse?
    5·2 answers
  • Reviewing old tests and quizzes will not help you determine what will be on a test because teachers don’t like to give students
    12·2 answers
  • Mac and Tosh are arguing in the cafeteria. Mac says that if he flings the Jell-O with a greater speed it will have a greater ine
    13·1 answer
  • Which shows a vector quantity in the given situation. The airplane was flying 500 miles per hour to west from New York to Califo
    12·2 answers
  • A horizontail rod (oriented in the east -west direction) is moved northward at a constant velocity through a magnetic field that
    11·1 answer
  • 6 A test of a driver's perception/reaction time is being conducted on a special testing track with level, wet pavement and a dri
    13·1 answer
  • 1. Encontrar la densidad de una sustancia, Si pesa 459 g y ocupa un volumen de 34.5 cmɜ.
    10·1 answer
  • These pairs of forces are known as ____________-reaction pairs because one pushes against the other with an equal but opposite f
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!