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Chapter 10: Problem 1503

For the following questions, statement as well as the reason(s) are given. Each questions has four options. Select the correct option. (a) Statement \(-1\) is true, statement \(-2\) is true; statement \(-2\) is the correct explanation of statement \(-1\). (b) Statement \(-1\) is true, statement \(-2\) is true but statement \(-2\) is not the correct explanation of statement \(-1\) (c) Statement \(-1\) is true, statement \(-2\) is false (d) Statement \(-1\) is false, statement \(-2\) is true Statement \(-1:\) Two waves moving in a uniform string having uniform tension cannot have different velocities. Statement \(-2:\) Elastic and inertial properties of string are same for all waves in same string. Moreover speed of wave in a string depends on its elastic and inertial properties only. (A) a (B) \(b\) (C) \(c\) (D) \(\mathrm{d}\)

Short Answer

Expert verified
The correct answer is (A) a.

Step by step solution

01

Evaluate the truth value of Statement \(-1\)#

Statement \(-1\) states that "Two waves moving in a uniform string having uniform tension cannot have different velocities". This statement is true because the velocity of a wave in a string depends on the tension and mass density of the string. If the string is uniform and has uniform tension, the velocity of any wave traveling through that string will be the same.
02

Evaluate the truth value of Statement \(-2\) #

Statement \(-2\) states that "Elastic and inertial properties of string are same for all waves in the same string. Moreover, the speed of the wave in a string depends on its elastic and inertial properties only." This statement is true as well. The velocity of a wave in a string depends on the square root of the ratio of tension (elastic property) and mass density (inertial property) of the string. As a result, if these properties are the same for all waves in the same string, their velocities will be the same as well.
03

Determine if Statement \(-2\) is the correct explanation for Statement \(-1\) #

Statement \(-1\) claims that in a uniform string with uniform tension, two waves cannot have different velocities. Statement \(-2\) explains that the elastic and inertial properties of the string are the same for all waves, and the speed of the wave depends on these properties only. Thus, statement \(-2\) does provide a correct explanation for statement \(-1\). Based on the analysis, statement \(-1\) is true, statement \(-2\) is true, and statement \(-2\) is the correct explanation for statement \(-1\). Therefore, we can conclude the correct option is: (A) a

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