Sinusoidal waves 5.00 cm in amplitude are to be transmitted along a string that has a linear mass density of 4.00 10-2 kg/m. The source can deliver a maximum power of 275 W, and the string is under a tension of 121 N. What is the highest frequency f at which the source can operate?

Respuesta :

Answer:

50.4 Hz

Explanation:

A = amplitude of the wave = 5 cm = 0.05 m

ÎĽ = linear mass density = 0.04 kg/m

P = maximum power delivered by source = 275 Watt

T = tension force in the string = 121 N

Speed of the wave is given as

[tex]v=\sqrt{\frac{T}{\mu }}[/tex]

[tex]v=\sqrt{\frac{121}{0.04 }}[/tex]

[tex]v[/tex] = 55 m/s

maximum power is given as

[tex]P = \frac{\mu (2\pi f)^{2} A^{2}v}{2}[/tex]

[tex]275 = \frac{(0.04) (2(3.14) f)^{2} (0.05)^{2}(55)}{2}[/tex]

[tex]f[/tex] = 50.4 Hz