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Chapter 16: Q16P (page 473)

The speed of a transverse wave on a string is170m/swhen the string tension is 120N. To what value must the tension be changed to raise the wave speed to180m/s?

Short Answer

Expert verified

The value of change in tension to raise the velocity to 180 m/s in wave speed is 135 N

Step by step solution

01

The given data

  • Speed of the wave,v1=170m/s
  • Tension in the string, T1=120N
  • Speed of the wave,v2=180m/s
02

Understanding the concept of the wave equation

The wave speed in a string will be equal to the square root of tension in the string having unit linear density.

Formula:

The velocity of a wave in terms of tension and linear density,v=Tμ (i)

03

Calculations the change in tension

First, we find the linear density of the string from the tension 120 N when the wave speed is 170 m/s.

Again, as the value of linear density is same for the given string. Hence, considering equation (i), we can compare the two velocities, hence

To find the tension in the string when wave speed is 180 m/s we can use the formula

T2=v22×μ=v22v12T1∵μ=T1v12=180170×120=134.5N≈135N

Hence, the value of tension should be changed to 135 N

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Most popular questions from this chapter

What is the speed of a transverse wave in a rope of length2.00 mand mass60.0 gunder a tension of 500 N?

A sinusoidal transverse wave traveling in the positive direction of an xaxis has amplitude of 2.0 cm , a wavelength of 10 cm , and a frequency of 400 Hz. If the wave equation is of the form y (x,t) =ymsin(kx±ωt), what are (a) role="math" localid="1660983337674" ym, (b) k , (c)ω , and (d) the correct choice of sign in front of ω? What are (e) the maximum transverse speed of a point on the cord and (f) the speed of the wave?

A string along which waves can travel is2.70 mlong and has a mass of 260 g. The tension in the string is 36.0 N. What must be the frequency of traveling waves of amplitude 7.70 mmfor the average power to be 85.0 W?

Consider a loop in the standing wave created by two waves (amplitude 5.00 mmand frequency 120 Hz ) traveling in opposite directions along a string with length 2.25 mand mass125gand under tension 40 N. At what rate does energy enter the loop from (a) each side and (b) both sides? (c) What is the maximum kinetic energy of the string in the loop during its oscillation?

Figure 16-32 shows the transverse velocity u versus time t of the point on a string at x = 0 , as a wave passes through it. The scale on the vertical axis is set by us=4.0m/s . The wave has the form y(x,t)=ymsin(kx-ωt+ϕ) . What then is ϕ ? (Caution:A calculator does not always give the proper inverse trig function, so check your answer by substituting it and an assumed value of ω into y(x,t)and then plotting the function.)
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