1) A steel guitar string is streched between supports 85.2 cm apart. When the temperature is 0 °C, the fundamental frequency of transverse oscillations of the string is 201.5 Hz. What will be the value of fundamental frequency in Hz if the temperature is raised to 53.6 °C? (Error of answer is tolerated within ±0.1 Hz, Do not include units in the answer box)

Useful Data:

mass density of steel is: 7,860 kg/m³

Young’s modulus of steel is 200,000,000,000 N/m² (20×10¹⁰ N/m²)

Coefficient of thermal expansion of steel is: 0.000011 (C°)^-1

2) Assume you have a diatomic gas initially at pressure p₀ and initial volume V₀. If you compress the gas isothermally to a 71.6% of its initial volume, the final pressure is p₁. If you compress it adiabatically to same final volume, the final pressure is p₂. What is the ratio p₁/p₂?

3) You can excite waves in a string of length 1.821 m fixed at both ends. You started from an arbitrarily low frequency and increased it slowly. You found two successive harmonic standing waves of frequencies: 214.7 Hz and 225.5 Hz. What is the speed of the wave in the medium in m/s.

Note that the speed of standing waves is zero, because it is composed of two waves of velocities v and –v. The question is about the magnitude of v and the answer is not zero!