Physics · Ch 8 — Sound
Newton's formula for velocity of sound
Newton's formula for velocity of sound
Isaac Newton was the first to study how a longitudinal (sound) wave's speed relates to the medium's properties. Because sound propagates as alternating compressions (denser regions) and rarefactions (less dense regions), its speed must depend on the medium's elasticity and its density. Newton proposed
where E is the medium's proper elasticity modulus and ρ is its density. Newton further assumed that as sound propagates, the medium's AVERAGE temperature stays constant throughout -- i.e. that sound propagation in air is an isothermal process -- so the relevant elastic modulus to use is the ISOTHERMAL bulk modulus, which for a gas equals simply the ambient pressure P itself. That specialises Newton's formula, for air, to
…
Worked out. A listener sits 150 m from the speakers at an outdoor concert, while a friend listens to the SAME concert via a live radio broadcast that has to travel 3000 km (an electromagnetic signal, travelling at the speed of light, 3x10^8 m/s) to reach them; the speed of sound in air is given as 330 m/s. The question asks who hears the music first and by how much. The method computes the sound-travel time for the nearby listener as distance/speed = 150/330 ≈ 0.4546 s, and the EM-signal travel time for the distant friend as 3000 km / (3x10^8 m/s) = 3x10^6 m / 3x10^8 m/s = 0.01 s, concluding the distant friend (listening via the near-instantaneous radio broadcast) hears the music FIRST, by a margin of 0.4546 - 0.01 = 0.4446 s -- a vivid illustratio …