Waves and its Characteristics: Practice Problem & Solution
Assertion (A): Two waves moving in a uniform string having uniform tension cannot have different velocities. Reason (R): Elastic and inertial properties of string are same for all waves in same string. Moreover, velocity of wave in a string depends on its elastic and inertial properties only.
Short Solution (Best for NEET):
To solve this problem, we apply the core principles of Waves and its Characteristics. Understanding the underlying formula is key to arriving at the correct answer below:
The speed of a transverse wave on a string is given by \( v = \sqrt{T/\mu} \), where \( T \) is the tension (elastic property) and \( \mu \) is the linear mass density (inertial property). If the string is uniform (constant \( \mu \)) and has uniform tension (constant \( T \)), then \( v \) must be constant for all waves propagating on it. Both A and R are true, and R correctly explains A.
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