Step 1: A sonometer wire of mass per unit length m = 2.0 g/m is stretched with tension T = 49 N. Resonance with a tuning fork occurs at vibrating length l = 32.0 cm. Find the fork's frequency. Step 2: Convert: m = 2.0×10⁻³ kg/m, l = 0.320 m. Step 3: Wave speed on the wire: v = √(T/m) = √(49/2.0×10⁻³) = √24500 ≈ 156.5 m/s. Step 4: Fundamental frequency of length l: n = v/(2l) = 156.5/(2 × 0.320) = 156.5/0.640 ≈ 244.5 Hz. Step 5: At resonance the fork's frequency N equals the wire's frequency n. Result: N ≈ 245 Hz. (A standard fork marked 256 Hz would resonate at a slightly shorter length — sliding the bridge until the paper rider dances off pinpoints it.)