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Sound

Sound. Mach and doppler. Mach Speed. Subsonic speeds are less than the speed of sound, whereas supersonic speeds are faster than sound. (Supersonic flights restricted over water).

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Sound

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  1. Sound Mach and doppler

  2. Mach Speed • Subsonic speeds are less than the speed of sound, whereas supersonic speeds are faster than sound. (Supersonic flights restricted over water). • Ernest Mach was an Austrian physicist (1838-1916), who in 1877 published a scientific paper on the principles of supersonics. • He also came up with the Mach number, which is the ratio of the velocity of an object to the velocity of sound. • A plane traveling at the speed of sound, therefore, has a Mach number of 1.

  3. Mach Speed • It's important to note that Mach 1 doesn't simply stand for the speed of sound, but rather the speed of an object traveling at the speed of sound. • Many deaths occurred until Chuck Yeager’s breakthrough flight with the Bell XS-1 Rocket plane of a supersonic speed on October 14th in 1947, in California. (Many planes could not handle the “wall of air” at Mach 0.8, that occurs.) • Mach 25 was achieved by the Shuttle Columbia where the speed of sound was 300 m/s.

  4. Example • Calculate an airplane’s speed if it moves at Mach 2.5 and the speed of sound at that location is 320 m/s. vsource = 2.5 (320 m/s) = 8.0 x 102m/s When an object exceeds the sound barrier: a sonic boom is heard. The craft catches up to the compressions of sound it creates which pile up to create a high pressure region. Crafts are designed to handle this.

  5. Doppler effect • The effect of frequency shift due to relative velocities was proposed by Johann Christian Doppler in 1842, but was verified experimentally in 1845 by Buys Ballot. • A moving sound source approaches a stationary observer and emits a frequency ƒo (the frequency we would hear at rest) and the observer would receive more waves every second as the source gets closer. • The observer hears an apparent rise in frequency that increases as the source approaches (and decreases as it recedes). (Ambulance sirens)

  6. Doppler effect • A formula can calculate this using v as the velocity of sound, vs as the velocity of the source, vo as the velocity of the observer and ƒ as the apparent frequency heard: • The formula is shown with vectors if the source and observer approach each other. If the directions change, the sign must be changed also.

  7. Doppler effect • A car travels at 100. km/h and sounds its horn at a stationary hitchhiker on the road. The horn’s actual frequency is 440.0 Hz and the air temperature is 0.00oC. What is the apparent frequency heard by the observer as the source a) approaches and b) moves away? • a) At 0oC, the speed of sound is defined as 332 m/s. • vs = 100 km/h (1000 m/km)/(3600s/h) = (100/3.6)m/s

  8. Doppler effect • a) At 0oC, the speed of sound is defined as v = 332 m/s. • vs = 100 km/h (1000 m/km)/(3600s/h) = (100/3.6)m/s, vo = 0 = 440 Hz[332 m/s + 0] [332 m/s – 100/3.6 m/s] = 480 Hz b) Denominator becomes addition so f = 406 Hz.

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