Sinusoidal waves 5.00 cm in amplitude are to be transmitted along a string having a linear mass density equal to 4.00 × 10-2 kg / m. If the source can deliver a maximum power of 90 W and the string is under a tension of 100 N, then the highest frequency at which the source can operate is (take π2=10 ):

Question

Sinusoidal waves 5.00 cm in amplitude are to be transmitted along a string having a linear mass density equal to 4.00 × 10-2 kg / m. If the source can deliver a maximum power of 90 W and the string is under a tension of 100 N, then the highest frequency at which the source can operate is (take π2=10 ): (A) 45.3 Hz (B) 50 Hz (C) 30 Hz (D) 62.3 Hz

Tardigrade Admin · Accepted Answer

We use power transmitted is given as P=(1/2) μ ω2 A2 V using V=√(T/μ) ⇒ P=(1/2) ω2 A2 √T μ ⇒ ω=√(2 P/A2 √T μ) ⇒ f=(ω/2 π)=(1/2 π) √(2 P/A2 √T μ) =30 Hz

45.3 Hz

50 Hz

30 Hz

62.3 Hz

We use power transmitted is given as P=21​μω2A2V using V=μT​​ ⇒P=21​ω2A2Tμ​ ⇒ω=A2Tμ​2P​​ ⇒f=2πω​=2π1​A2Tμ​2P​​ =30Hz

We use power transmitted is given as
$P = \frac{1}{2} μ ω^{2} A^{2} V$ using $V = \frac{T}{μ}$
$\Rightarrow P = \frac{1}{2} ω^{2} A^{2} T μ$
$\Rightarrow ω = \frac{2 P}{A ^{2} T μ}$
$\Rightarrow f = \frac{ω}{2 π} = \frac{1}{2 π} \frac{2 P}{A ^{2} T μ}$
$= 30 Hz$