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## Finding Mass of an Astronaut in Space

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**Finding Mass of an Astronaut in Space**This device consists of a spring-mounted chair in which the astronaut sits. The chair is then started oscillating in simple harmonic motion. The period of the motion is measured electronically and is automatically converted into a value of the astronaut’s mass, after the mass of the chair is taken into account. The spring used in one such device has a spring constant of 606 N/m, and the mass of the chair is 12.0 kg. The measured oscillation period is 2.41 s. Find the mass of the astronaut. (students work this.)**Example 1 The Wavelengths of Radio Waves**AM and FM radio waves are transverse waves consisting of electric and magnetic field disturbances traveling at a speed of 3.00x108m/s. (What is this number?) A station broadcasts AM radio waves whose frequency is 1230x103Hz and an FM radio wave whose frequency is 91.9x106Hz. Find the distance between adjacent crests in each wave.**16.2 Periodic Waves**Example 1 The Wavelengths of Radio Waves AM and FM radio waves are transverse waves consisting of electric and magnetic field disturbances traveling at a speed of 3.00x108m/s. A station broadcasts AM radio waves whose frequency is 1230x103Hz and an FM radio wave whose frequency is 91.9x106Hz. Find the distance between adjacent crests in each wave.**16.2 Periodic Waves**AM FM**Problem**• Light travels at 3 * 10 8 m/s. Sound travels at 331 m/s. • If lightning strikes 8.2km away from you, how long passes before you see it? • How long passes until you hear it? • (students work this.)**Problem**• Light travels at 3 * 10 8 m/s. Sound travels at 331 m/s. • V = d/t => t = d/v • If lightning strikes 8.2km away from you, how long passes before you see it? • t = d/v = 8200m / 3 * 10 8 m/s • How long passes until you hear it? • t = d/v = 8200m / 331 m/s • (students work this.)**Problem**• So you see lightning hit 1 mile away, how many seconds do you count before you hear it? • (students work this.)**Problem**• So you see lightning hit 1 mile away, how many seconds do you count before you hear it? • t = d/v = 1609m / 331 m/s • So each 5 sec is about 1 mile away. • Each 1 sec is about 3 football fields away. • (Talk about military timing of artillery and nukes.)**THE PRINCIPLE OF LINEAR SUPERPOSITION**When two or more waves are present simultaneously at the same place, the resultant disturbance is the sum of the disturbances from the individual waves.**Constructive Interference**• Two waves, a and b, have the same frequency and amplitude • Are in phase • The combined wave, c, has the same frequency and a greater amplitude**Destructive Interference**• Two waves, a and b, have the same amplitude and frequency • They are half a cycle out of phase • When they combine, the waveforms cancel**Reflection of Waves – Fixed End**• Whenever a traveling wave reaches a boundary, some or all of the wave is reflected**Reflection of Waves – Fixed End**• Whenever a traveling wave reaches a boundary, some or all of the wave is reflected • When it is reflected from a fixed end, the wave is inverted • The shape remains the same**What happens when a wave interferes with its own reflection?**• Sometimes we get standing waves.**The a string will only allow certain wavelengths to be**standing waves. • Because the endpoints need to be nodes. • For a string with two fixed ends, • λ= 2L / n n = 1, 2, 3, 4 …….