A sinusoidal wave of frequency f travels from a string of linear density μ₁ to another string of linear density μ₂. Both strings are under the same tension. Which relation correctly gives the ratio of transmitted wavelength λ₂ to incident wavelength λ₁?
Options

Question

A sinusoidal wave of frequency f travels from a string of linear density μ₁ to another string of linear density μ₂. Both strings are under the same tension. Which relation correctly gives the ratio of transmitted wavelength λ₂ to incident wavelength λ₁?

Options

G1 Physics · Accepted Answer

Frequency remains unchanged across the junction: f₂ = f₁. Wave speed on a string is v = √(T/μ). Therefore, v₂/v₁ = √(μ₁/μ₂). Since λ = v/f and f is unchanged, λ₂/λ₁ = v₂/v₁ = √(μ₁/μ₂). Correct option: B.