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

Amplitude changes by factor of 2 means double.

Step-by-step 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 = (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 √(P)`

Where
`k =` constant

Here Power become quadruple means four times,

`A = √(4P)`

`A = 2√(P)`

So amplitude changes by factor of 2 means double