A power source is going to shake a string and create waves 5.0 cm in amplitude. The string has a linear mass density of 4.0x10-2 kg/m and is pulled under a tension of 100 N. The source can deliver a maximum power of 300 W. What is the highest frequency f at which the source can shake without exceeding the maximum power?

55.13 Hz

Explanation:

Given that :

Amplitude, A =. 5cm = 0.05m

Density, d = 4 * 10^-2

Tension, T = 100N

Power = 300 W

Recall:

Power = 0.5dA²w²v

v = velocity = √T/d ; w = Angular velocity = 2πf

Rewriting our equation :

P = 0.5 * d * A² * (2πf)² * √T/d

300 = 0.5 *(4*10^-2)* 0.05² * 4π² * f² * sqrt(100/0.04)

300 = 0.5*(4*10^-2) * 0.05² * 4π² * f² * sqrt(2500)

300 = 0.02 * 50 * 0.05² * 39.478417 * f²

300 = 0.0986960 * 0.05² * f²

f² = 300 / 0.0986960

f² = 3039.6355

f = sqrt(189.97722)

f = 55.132889

= 55.13 Hz

fgravity=10x10=100n case 1

fgravity=30x20=600n case 2

6 times more