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Chapter 16: Q. 2 (page 451)

The wave speed on a string is 150 m/s when the tension is 75 N. What tension will give a speed of 180 m/s?

Short Answer

Expert verified

The tension of the string is 108 N

Step by step solution

01

Step 1. Write the given information

The speed of the wave is given by v1= 150m/s

The tension of the string is T2=75N

The tension of the string is changed

The new speed of the string is v2= 180m/sec

02

Step 2. To determine the new tension of the string

The formula for the speed of the wave is given by

v=Tμ

Here µ is the effective mass of the string

As it can be observed that the speed is directly proportional to the square root of tension of the string

v∝T

The new tension is given by
v1v2=T1T2
substitute the values,

localid="1649317557949" role="math" 150m/s180m/s=75NT21501802=75NT2T2=75N(180×180)150×150T2=108N

Therefore, the tension of the string is 108 N

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