Question

I stretch a rubber band and "plunk" it to make it vibrate at its fundamental frequency. I then stretch it to twice its length and make it vibrate at the fundamental frequency once again. The rubber band is made so that doubling its length doubles the tension and reduces the mass per unit length to half of its original value. The new frequency will be related to the old by a factor as ________.

1) 1.0
2) 1.4
3) 2.0
4) 2.5
5) 4.0

Answer 1

The new frequency of a rubber band stretched to twice its original length, with doubled tension and halved mass per unit length, will be 1.4 times the original frequency.

Step-by-step explanation:

When a rubber band is stretched to twice its length, while the tension also doubles and the mass per unit length is halved, the change in the fundamental frequency can be determined using the formula for the frequency of a vibrating string f = (1/2L) * sqrt(T/μ), where L is the length, T is the tension, and μ is the mass per unit length. After doubling the length (L) and tension (T), and halving the mass per unit length (μ), we can deduce that the new frequency will be related to the old frequency by a factor of sqrt(2) since f_new = (1/(2 * 2L)) * sqrt(2T/(0.5μ)) = (1/2L) * sqrt(T/μ) * sqrt(2) = f_old * sqrt(2). Therefore, the new frequency will be 1.4 times the old frequency, which means the correct answer to this question is option 2) 1.4.