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Chapter 16: Q28P (page 474)

Use the wave equation to find the speed of a wave given by -

y(x,t)=(3.0mm)sin[(4.00m-1)x鈥�(7.00s-1)t].

Short Answer

Expert verified

The speed of the wave is 1.75 m/s

Step by step solution

01

The given data

The given equation for the wave,y(x,t)=(3.0mm)sin[(4.00m-1)x鈥�(7.00s-1)t]

02

Understanding the concept of the wave equation

The solution of wave equation is given by,

y(x,t)=ymsin(kx-蝇t)

By comparing this equation with the given equation, we can calculate the speed of the given wave.

Formula:

The speed of the wave,v=蝇/k (i)

03

Calculation of the speed of wave

By comparing the given equation with the solution of the wave equation

y(x,t)=(3.0mm)sin[(4.00m-1)x鈥�(7.00s-1)t]

Comparing the given equation with general that is,yx,t=ymsinsinkx-wt we get

We can get, angular frequency,蝇=7.00rad/s

Wave number,k=4.00/rad

Using equation (i), we get the speed of the wave as

v=7.00s-14.00m-1=1.75m/s

Hence, the value of the speed of the wave is1.75m/s

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Most popular questions from this chapter

A sinusoidal wave of frequency 500 Hzhas a speed of 350 m/s . (a)How far apart are two points that differ in phase by蟺/3rad ? (b)What is the phase difference between two displacements at a certain point at times 1.00 msapart?

A 100 gwire is held under a tension of 250 Nwith one end at x = 0and the other at x = 10.0 m. At time t = 0, pulse 1is sent along the wire from the end at x = 10.0 m. At time t = 30.0 ms, pulse 2is sent along the wire from the end at x = 0.At what position xdo the pulses begin to meet?

At timet = 0and at position x = 0 malong a string, a traveling sinusoidal wave with an angular frequency of 440 rad/shas displacement y=+4.5mmand transverse velocityu=0.75m/s . If the wave has the general formy(x,t)=ymsin(kx-蝇t+蠒) , what is phase constant 蠒?

Use the wave equation to find the speed of a wave given by 鈥� y(x,t)=(2.00mm)[20m-1x鈥�4.0s-1t]0.5.

Figure 16-44 shows the displacement yversus time tof the point on a string atx=0, as a wave passes through that point. The scale of the yaxis is set byys=6.0mm. The wave is given byy(x,t)=ymsin(kx-蝇t-蠒). What is胃? (Caution:A calculator does not always give the proper inverse trig function, so check your answer by substituting it and an assumed value of蝇intoy(x,t)) and then plotting the function.)
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