Question

A source vibrating at constant frequency generates a sinusoidal wave on a string under constant tension. If the power delivered to the string is quadrupled, by what factor does the amplitude change? 16

Answer 1

Answer:

Amplitude changes by factor of 2 means double.

Explanation:

Given:

If the power delivered to the string is quadrupled.

From the formula of power transmitted by a sinusoidal wave on a stretched string is,

  $P = \frac{1}{2} \mu \omega ^{2} A^{2} v$

Where $\mu =$ mass per unit length, $\omega =$ angular speed, $A =$ amplitude, $v =$ wave speed, $P =$ power delivered.

Here we need only two terms power and amplitude.

       $P$∝ $A^{2}$

All other quantities are constant for our problem,

     $A = k \sqrt{P}$

Where $k =$ constant

Here Power become quadruple means four times,

     $A = \sqrt{4P}$

     $A = 2\sqrt{P}$

So amplitude changes by factor of 2 means double