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Chapter 7: Q25P (page 345)

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脳108m/sec

Short Answer

Expert verified

The equation for a sinusoidal radio wave is y=10sin1200脳103蟺x3脳108-t.

Step by step solution

01

Given data

The dimensions are given as follows:

Amplitude,A=10. .

Frequency,f=600kilohertz.

Velocity,c=3脳108m/sec.

02

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 asAsin(2蟺(ft+蠒))

03

Calculation to find the dimension of the wave equation

Following is a standard wave equation, y=Asin2蟺位(x-vt)

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

So, (distance)=(speed)(time)

位=vT

Since,

T=1f位=vf

Hence, v=位f.

04

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

Now, solve the wave equation as follows:

y=Asin2蟺位(x-vt)y=Asin2蟺惫位xv-t

Since, v=位蹿.

y=Asin2蟺(位蹿)位xv-ty=Asin2蟺蹿xv-t

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

y=10sin1200脳103蟺x3脳108-t

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Most popular questions from this chapter

(a) Represent as an exponential Fourier transform the function

f(x)={sinx,0<x<蟺0,otherwise

Hint: write sinxin complex exponential form.

(b) Show that your result can be written as

f(x)=1蟺鈭�0鈭�cos伪x+cos伪(x鈭�蟺)1鈭�伪2d伪.

Sketch several periods of the corresponding periodic function of period 2蟺. Expand the periodic function in a sine-cosine Fourier series.

f(x)=0,-蟺<x<01,0<x<蟺2,0,蟺2<x<蟺.

Normalize f(x)in Problem 21; that is find the factor Nso that 鈭�鈭�鈭�鈭�|Nf(x)|2=1.Let 蠄(x)=Nf(x), and find 蠒(p)as given in Problem 35. Verify Parseval鈥檚 theorem, that is, show that鈭�鈭�鈭�鈭�|蠒(p)|2dp=1.

In Problems 17to 20, find the Fourier sine transform of the function in the indicated problem, and write f(x)as a Fourier integral [use equation (12.14)]. Verify that the sine integral for f(x)is the same as the exponential integral found previously.

Problem 12

Use Parseval鈥檚 Theorem and the results of the indicated problems to find the sum of the series in Problems 5to 9

The series 132+1152+1352+..., using Problem 5.11
See all solutions

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