Intelligent assessment and revision tools for OCR A Physics

In a lab sonometer, a steel string of length L is fixed at both ends and under tension T. It is driven at a clear third-harmonic resonance with frequency f3. A light clamp is then added exactly at the midpoint to hold that point stationary, and at the same time the tension is increased to 2T. The driver is swept to find the lowest-frequency resonance of the modified setup. Compared with the original f3, what is the new resonance frequency, and why?

• A It decreases to about 0.94 f3, because the clamp forces a node at the centre so the lowest allowed mode is n = 2, and doubling T increases the wave speed by a factor √2.
• B It increases to about 1.33 f3, because the clamp makes the lowest allowed mode n = 2 and doubling T doubles the wave speed.
• C It decreases to about 0.67 f3, because moving from the third to the second harmonic lowers the frequency by 2/3 and the wave speed is unchanged.
• D It stays approximately at f3, because clamping the midpoint just splits the string into two halves each resonating at its own fundamental, matching the previous third harmonic.