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Chapter 7: Q24P (page 345)

The velocity of sound in sea water is about 1530m/sec. Write an equation for a sinusoidal sound wave in the ocean, of amplitude 1 and frequency1000hertz .

Short Answer

Expert verified

The equation for a sinusoidal sound wave is y=sin2000蟺x1530-t.

Step by step solution

01

Given data

The dimensions are given as follows:

Amplitude,A=1.

Frequency, f=1000hertz.

Velocity,v=1530m/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 .

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v位xv-t

Since,(v=位f). .

y=Asin2蟺(位f)位xv-ty=Asin2蟺fxv-t

Now, substitute all the value in above equation as follows:

y=sin2000蟺x1530-t

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Most popular questions from this chapter

Write out the details of the derivation of equation 5.10.

We have said that Fourier series can represent discontinuous functions although power series cannot. It might occur to you to wonder why we could not substitute the power series for sinnxand cosnx(which converge for all x) into a Fourier series and collect terms to obtain a power series for a discontinuous function. As an example of what happens if we try this, consider the series in Problem 9.5. Show that the coefficients of x, if collected, form a divergent series; similarly, the coefficients of x3form a divergent series, and so on.

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