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Lapatulllka [165]
3 years ago
8

Using the method of dimension, derive an expression for the velocity of sound waves. assume that the velocitu depends on:

Physics
1 answer:
Soloha48 [4]3 years ago
7 0

Answer:

v = K √(E / ρ)

Explanation:

Modulus of elasticity has units of N/m², or kg/m/s².

Density has units of kg/m³.

Velocity has units of m/s.

If we divide modulus of elasticity by density, we can eliminate kg:

E / ρ = [kg/m/s²] / [kg/m³]

E / ρ = [m²/s²]

Taking the square root gets us units of velocity:

√(E / ρ) = [m/s]

Multiply by the constant K:

v = K √(E / ρ)

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To practice Problem-Solving Strategy 30.1: Inductors in Circuits. A circuit has a 1 V battery connected in series with a switch.
ki77a [65]

Answer:

0.0133A

Explanation:

Since we have two sections, for the Inductor region there would be a current i_1. In the case of resistance 2, it will cross a current i_2

Defined this we proceed to obtain our equations,

For i_1,

\frac{di_1}{dt}+i_1R_1 = V

I_1 = \frac{V}{R_1} (1-e^{-\frac{R_1t}{L}})

For i_2,

I_2R_2 =V

I_2 = \frac{V}{R_2}

The current in the entire battery is equivalent to,

i_t = I_1+I_2

i_t = \frac{V}{R_2}+\frac{V}{R_1} (1-e^{-\frac{R_1t}{L}})

Our values are,

V=1V

R_1 = 95\Omega

L= 1.5*10^{-2}H

R_2 =360\Omega

Replacing in the current for t= 0.4m/s

i=\frac{1}{360}+\frac{1}{95}(1-e^{-\frac{95*0.4}{1.5*10^{-2}}})

i= 0.0133A

i_1 = 0.01052A

3 0
3 years ago
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