Sinusoidal waves 5 mm in amplitude are to be transmitted along a string having a linear mass density equal to 4 × 10⁻² kg m⁻¹. If the source can deliver an average power of 90 W and the string is under a tension of 100 N, then find the frequency (in Hz) at which the source can operate. (Take π² = 10)
Physics · Wave Motion
JEE Mains Advanced

Question

Sinusoidal waves 5 mm in amplitude are to be transmitted along a string having a linear mass density equal to 4 × 10⁻² kg m⁻¹. If the source can deliver an average power of 90 W and the string is under a tension of 100 N, then find the frequency (in Hz) at which the source can operate. (Take π² = 10)

Physics · Wave Motion

G1 Physics · Accepted Answer

Step 1: v = √(T/μ)=√(100/0.04)=50 m s⁻¹. Step 2: P̄ = ½ μω²A²v = 90 W with A=5×10⁻³ m. Solving gives ω=600π rad s⁻¹ using π²≈10, hence f=ω/2π=300 Hz.