A mechanical wave driver in an intro physics lab experiment drives a string at frequency $f$ with amplitude $A.$ At these settings, the wave driver delivers a time$-$averaged power $P_{\text{a}\text{v}\text{g}}$ to the string.

The lab manual instructs a student to increase the frequency of oscillation by a factor of $70$ and then measure the new amplitude of oscillation precisely. Upon measuring the amplitude, the student discovers it decreased by a factor of $2\mathrm{.}85.$

Based on the student's measurements, express the new time$-$averaged power $P_{\text{n}\text{e}\text{w}}$ delivered to the string in terms of the original power by calculating the porportionality constant $b$ in the equation

$P_{\text{n}\text{e}\text{w}}=b{P}_{\text{a}\text{v}\text{g}}$

$b=$

If the tension in the string is then increased, how does the power delivered to the string change?

It increases.

It decreases.

It remains the same.