Chapter 7: Q25P (page 345)

Write an equation for a sinusoidal radio wave of amplitude 10 and frequency $600 kilohertz$ . Hint: The velocity of a radio wave is the velocity of light, $c = 3 \times 10^{8} m / \sec$

Short Answer

Expert verified

The equation for a sinusoidal radio wave is $y = 10 \sin [1200 \times 10^{3} π (\frac{x}{3 \times 10^{8}} - t)]$ .

Step by step solution

Given data

The dimensions are given as follows:

Amplitude, $A = 10 .$ .

Frequency, $f = 600 k i l o h e r t z .$

Velocity, $c = 3 \times 10^{8} m / s e c .$

Concept of Sinusoidal sound wave

The trigonometric cosine function can be used to explain a sinusoid's unique functional form, and the most fundamental sinusoid can be written as $A \sin (2 π (ft + ϕ))$

Calculation to find the dimension of the wave equation

Following is a standard wave equation, $y = A \sin (\frac{2 π}{λ} (x - v t))$

Time period is the time required to travel a distance of $λ$ .

So, $(d i s \tan c e) = (s p e e d) (t i m e)$

$λ = v T$

Since,

$T = \frac{1}{f} λ = \frac{v}{f}$

Hence, $v = λ f .$

Put the value of the obtained dimensions in the sinusoidal wave equation

Now, solve the wave equation as follows:

$y = Asin (\frac{2 π}{λ} (x - vt)) y = Asin (\frac{2 πv}{λ} (\frac{x}{v} - t))$

Since, $v = λf .$

$y = Asin \frac{2 π (λf)}{λ} (\frac{x}{v} - t) y = Asin 2 πf (\frac{x}{v} - t)$

Now putting all the value in the above equation as follows:

$y = 10 \sin [1200 \times 10^{3} π (\frac{x}{3 \times 10^{8}} - t)]$

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Write an equation for a sinusoidal radio wave of amplitude 10 and frequency $600 kilohertz$ . Hint: The velocity of a radio wave is the velocity of light, $c = 3 \times 10^{8} m / \sec$

Short Answer

Step by step solution

Given data

Concept of Sinusoidal sound wave

Calculation to find the dimension of the wave equation

Put the value of the obtained dimensions in the sinusoidal wave equation

One App. One Place for Learning.

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Write an equation for a sinusoidal radio wave of amplitude 10 and frequency600kilohertz. Hint: The velocity of a radio wave is the velocity of light,c=3×108m/sec

Short Answer

Step by step solution

Given data

Concept of Sinusoidal sound wave

Calculation to find the dimension of the wave equation

Put the value of the obtained dimensions in the sinusoidal wave equation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Nuclear Physics

Translational Dynamics

Electricity

Scientific Method Physics

Kinematics Physics

Magnetism

Study anywhere. Anytime. Across all devices.

Write an equation for a sinusoidal radio wave of amplitude 10 and frequency $600 kilohertz$ . Hint: The velocity of a radio wave is the velocity of light, $c = 3 \times 10^{8} m / \sec$