High School

If the mass per unit length of a violin string is quadrupled without changing the string's tension, what happens to the speed of a wave produced by bowing the string?

A. It becomes four times its former value.
B. It becomes one half of its former value.
C. It becomes two times its former value.
D. It becomes one quarter of its former value.
E. It does not change.

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.