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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

Two sinusoidal waves with the same amplitude and wavelength travel through each other along a string that is stretched along an xaxis. Their resultant wave is shown twice in Fig. 16-41, as the antinode Atravels from an extreme upward displacement to an extreme downward displacement in. The tick marks along the axis are separated by 10 cm; height His 1.80 cm. Let the equation for one of the two waves is of the form y(x,t)=ymsin(kx+ωt).In the equation for the other wave, what are (a)ym, (b) k, (c) ω, and (d) the sign in front ofω?

A125 cm length of string has mass 2.00 gand tension 7.00 N. (a) What is the wave speed for this string? (b)What is the lowest resonant frequency of this string?

Two sinusoidal waves of the same period, with amplitudes of 5.0and 7.0 mm, travel in the same direction along a stretched string; they produce a resultant wave with an amplitude of 9.0 mm. The phase constant of the 5.0 mmwave is 0.What is the phase constant of the 7.0 mmwave?

A 120 mlength of string is stretched between fixed supports. What are the (a) longest, (b) second longest, and (c) third longest wavelength for waves traveling on the string if standing waves are to be set up? (d)Sketch those standing waves.

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?
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