A student investigates stationary waves on a stretched string of a musical instrument.
Explain how a stationary wave is produced when a stretched string is plucked.
The vibrating length of the string is 0.40 m0.40 \text{ m}0.40 m. When the tension in the string is 64 N64 \text{ N}64 N, the string vibrates with a first-harmonic frequency of 250 Hz250 \text{ Hz}250 Hz. Calculate the mass of a 1.0 m1.0 \text{ m}1.0 m length of the string.
Determine the speed at which waves travel along this string when it vibrates with a first-harmonic frequency of 250 Hz250 \text{ Hz}250 Hz.
The tension in the string is directly proportional to its extension, with a stiffness (force per unit extension) of 4.0 N mm−14.0 \text{ N mm}^{-1}4.0 N mm−1. The string is further stretched by rotating a circular tuning peg of diameter 8.0 mm8.0 \text{ mm}8.0 mm through an angle of 45∘45^\circ45∘. Determine the new higher first-harmonic frequency produced. Assume that there is no change in the mass per unit length of the string.
25 exam-style questions on AQA A Level Physics Progressive and stationary waves, covering Progressive waves, Longitudinal and transverse waves, and Principle of superposition of waves and formation of stationary waves. Each one has a worked solution and a mark scheme showing where the marks go.