Wave speed formula exponents for tension and density

Steps:

• Rewrite v = sqrt(T/μ) as v = T^{1/2} μ^{-1/2}.
• Identify p as the exponent of T, so p = 1/2.
• Identify q as the positive exponent in the denominator for μ, so v ∝ T^p / μ^q with q = 1/2.
• Confirm by squaring: v^2 = T/μ, showing direct proportionality to T and inverse to μ.

Why C is correct:

• Matches the formula v = sqrt(T/μ), where exponents are +1/2 for T and -1/2 (or q=1/2 in denominator) for μ, per wave speed derivation from Newton's laws.

Why the others are wrong:

• A: q=1 implies v ∝ 1/μ, but formula shows sqrt(1/μ).
• B: p=1 implies v ∝ T, but formula shows sqrt(T).
• D: Incomplete option provides no valid exponents.

Final answer: C