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
What name is used for a high-power variable resistor?
const2013 [10]
The answer would be C: Rheostat.  :)
3 0
3 years ago
Read 2 more answers
The current produced in homes is ______ current.
Lelu [443]
If any current is PRODUCED in an individual home, like with
a windmill or solar panels, it is direct current (DC).

The current SUPPLIED to homes by the local utility company
is alternating current (AC).
8 0
3 years ago
Read 2 more answers
What is the lateral surface area of a cylinder with height of 7 m and a base diameter of 4 m (to the nearest whole number)?
yuradex [85]
2×22/7×2×7
44/7×2×7
44×2
88
8 0
3 years ago
Which of the following is true about inertia
Tamiku [17]

Answer:

The correct answers are It is the resistance of an object to changes in its motion, and It is a force

3 0
3 years ago
Which event happens in a solar cell when the photoelectric effect occurs?
KiRa [710]

Answer:

current forms when electromagnetic waves strike a semiconductor, removing some of its electrons.

Explanation:

7 0
2 years ago
Other questions:
  • I really don’t know what it is to me they r all the same
    11·2 answers
  • A large truck and a compct car are both driving down the
    15·1 answer
  • a train travels 99 kilometers in 3 hours, and then 80 kilometers in 5 hours. What is it’s average speed?
    8·1 answer
  • Describing Forms of Energy
    8·1 answer
  • Write down the equation that links energy transferred, charge flow, and<br> potential difference.
    14·1 answer
  • HELP MEH QUICK PLEASE
    13·1 answer
  • Look at the pic please
    8·1 answer
  • Find the resultant force And angle
    11·1 answer
  • A wave created by shaking a rope up and down is called a.
    10·1 answer
  • the fireman wishes to direct the flow of water from his hose to the fire at b. determine two possible angles u1 and u2 at which
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!