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?.

Answer 1

When the amplitude varies, it means twice as much.

Which instances of sinusoidal waves are there?

Simple harmonic motion, such the swinging of a pendulum or the weight of a weight on a spring, produces a sinusoidal relationship between position and time. Sound and water waves, for example, can be visualized as sinusoids.

Given:

if the string is given four times as much power.

According to the power that a sinusoidal wave on a stretched string transmits,

P =$\frac{1}{2}$ μω^A^2v

Where  μ=mass per unit length, w= angular speed, A= amplitude, v= wave speed, P= power delivered.

P ∝$A^{2}$

Here, the only terms we need are power and amplitude.

A =K$\sqrt{P}$

Where K is constant

Here, "power become quadruple" refers to four,

A = $\sqrt{4P}$

A =2 $\sqrt{P}$

Therefore, an increase in amplitude by a factor of two is equivalent to a twofold increase.

To know more about sinusoidal wave visit:-

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