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Answer :
When the mass per unit length of a violin string is quadrupled, the speed of the wave on the string b) becomes half of its former value.
If the mass per unit length of a violin string is quadrupled without changing the string's tension, the speed of a wave traveling on that string would be affected as per the formula for wave speed on a string, v = \\sqrt{T/\mu}, where T represents tension and \mu represents the mass per unit length. When the mass per unit length is quadrupled, the denominator of this fraction increases by a factor of four. Thus, since speed is proportional to the square root of 1/\mu, the speed of the wave would become half of its former value when the mass per unit length is quadrupled.
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