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Ivanshal [37]
3 years ago
8

Explain the 3 factors that affect the Speed of Sound

Physics
1 answer:
Alexxandr [17]3 years ago
3 0
Nature of media,Temperature frequency
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An undamped spring-mass system contains a mass that weighs and a spring with spring constant . It is suddenly set in motion at b
balandron [24]

Answer:

Explanation:

When all other forces acting on the mass in a damped mass-spring system are grouped together into one term denoted by F(t), the differential equation describing

motion is

Mx''+ βx' + kx = F(t).

Note for an undamped system

β=0,

Then, the differential equation becomes

Mx'' + kx = F(t).

The force is in the form

F=Fo•Sinωo•t

Let solved for the homogeneous or complementary solution, I.e f(t) = 0

Using D operator

MD² + k = 0

MD²=-k

D²=-k/M

Then, D= ±√(-k/m)

D=±√(k/m) •i

So we have a complex root

Therefore, the solution is

x= C1•Cos[√(k/m)t] + C2•Sin[√(k/m)]

This is simple harmonic motion that once again we prefer to write in the form

x(t) = A•Sin[ √(k/M)t + φ]

Where A=√(C1²+C2²)

and angle φ is defined by the equations

sin φ = C1/A and cos φ = C2/A.

Quantity √(k/M), often denoted by ω, is called the angular frequency.

This is called the natural frequency (ωn) of the system

ωn=√(k/M)

ωn²= k/M

Now, for particular solution

Xp=DSinωo•t

Xp' = Dωo•Cosωo•t

Xp"=-Dωo²•Sinωo•t

Now substituting this into

Mx'' + kx = F(t).

M(-Dωo²•Sinωo•t) + k(DSinωo•t)=FoSinωo•t

Now, let solve for D

D(-Mωo²•Sinωo•t +kSinωo•t) = FoSinωo•t

D=Fo•Sinωo•t/(-Mωo²•Sinωo•t +kSinωo•t)

D=Fo•Sinωo•t / Sinωo•t(-Mωo²+k)

D=Fo / (-Mωo²+k)

D=Fo / (k-Mωo²)

Divide through by k

D=Fo/k ÷ (1 -Mωo²/k)

Note from above

ωn²= k/M

Therefore,

D=Fo/k ÷ (1-ωo²/ωn²)

D=Fo/k ÷ [1-(ωo/ωn)²]

Then,

Xp=DSinωo•t

Xp=(Fo/k ÷ [1-(ωo/ωn)²]) Sinωo•t

Then the general solution is the sum of the homogeneous solution and particular solution

Xg(t)=(Fo/k ÷ [1-(ωo/ωn)²]) Sinωo•t + A•Sin[ √(k/M)t + φ]

Check attachment for the graph of homogeneous, particular and general solution.

Also, check for better way of writing the equations.

8 0
3 years ago
Which statement is true of AC current?. Select one of the options below as your answer:. . A.. It uses a battery as a power sour
Nonamiya [84]
<span>The answer is B. It can be converted from high to low voltage and vice versa using transformers. That is why high voltages (tens or hundreds of kilovolts) is used to efficiently transfer electricity for large distances and then converted to 110-240V.

The answer can also be derived by elimination. [A] is not right because battery provides only Direct Current (DC). [C] is not right because high voltages are used for AC (from 110V to hundreds of kilovolts). [D] is not right because as the name Alternating Current suggests, the current is alternating in its direction. [E] is not right because DC was the first type of current invented.</span>
8 0
3 years ago
Read 2 more answers
How are steam powered boats different from sailboats
Alex
Steam powered boats run from an engine, using power, gears, and cranks to function.

Sailboats use no engine and rely on winds to move and change the direction of the boat. 
3 0
3 years ago
Read 2 more answers
A jet travels 1000 kilometers in 5 hours. What is its average speed?
nlexa [21]

Given:

Total distance = 1000 kilometer

Total time = 5 hours

To find:

Average speed = ?

Formula used:

v_{avg} = \frac{s}{t}

Where v_{avg} = average speed

s = total distance

t = total time

Solution:

Average speed of the jet is given by,

v_{avg} = \frac{s}{t}

Where v_{avg} = average speed

s = total distance

t = total time

v_{avg} = \frac{1000}{5}

v_{avg} = 200 km/ h

Thus, average speed of the jet is 200 km/h.

Hence, Option (A) is correct.


7 0
3 years ago
How does the transfer of thermal energy occur?
natali 33 [55]
Heat<span> may be </span>transferred<span> by means of conduction, convection, or radiation. </span>
8 0
3 years ago
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