Question

Solve question
chapter :- Oscillations and waves .​

Answer 1

Answer:

Option (c ) 80m

Step-by-step explanation:

Given :- string is clamped at the both ends and it is vibrating Y = 0.3sin(0.157x )cos200πt

Comparing it with general equation of stationary wave . i.e Y = asinkxcosωt , We get ,

• K = (2π/λ ) = 0.157

• λ = 2π / 0.157 = 4π² [∵ 1/2π ≈ 0.157 ] _____(i)

• and ω = 200π = 2π/T

• => T = 1/20s

As the possible wavelength associated with nth harmomic of a vibrating string , i. e fixed at both ends is given as λ = 2l/n or, l = n(λ /2)

Now, According to question , String is fixed from both ends and oscillates in 4th harmonic , So

• 4(λ/2) = I => 2λ= I

l = 2 × 4π² = 8π² [using eq. (i) ]

Now, π² ≈ 10 => l = 80m Answer