8. How do longitudinal waves differ from transverse waves?Use a diagram and have example for each. 9. A plane flies at Mach2.2. How long does it take to fly across the Atlantic Ocean which is approximate 8.0times 10^3km across. (air temp=0^circ C) [3.1hrs] 10. A standing wave is produced on a 1.0 m spring with 5 nodes (including fixed ends). a. How many antinodes are there? [4] If the frequency of the source is 5.0Hz, what is the speed of the wave? [2.5m/s] 11. In a closed air column, a tuning fork of frequency 128Hz is struck and the temperature is 22^circ C a. Determine the first resonant length of the air column. [0.67m]

**8. Longitudinal vs. Transverse Waves:**<br /><br />* **Transverse Waves:** In transverse waves, the particle displacement is *perpendicular* to the direction of wave propagation. Think of shaking a rope up and down – the wave travels along the rope, but the particles of the rope move up and down.<br /><br /> * **Diagram:**<br /><br /> ```<br /> Wave propagation --><br /> /\ /\ /\<br /> / \ / \ / \<br /> / \ / \ / \<br /> _/______\/______\/______\<br /> Particle displacement<br /> ```<br /><br /> * **Example:** Light waves, waves on a string, seismic S-waves.<br /><br /><br />* **Longitudinal Waves:** In longitudinal waves, the particle displacement is *parallel* to the direction of wave propagation. Think of a sound wave – the air particles compress and expand along the direction the sound travels.<br /><br /> * **Diagram:**<br /><br /> ```<br /> Wave propagation --><br /> | ||| | ||| | ||| |<br /> | ||| | ||| | ||| |<br /> | ||| | ||| | ||| | Compression/Rarefaction<br /> ```<br /><br /> * **Example:** Sound waves, seismic P-waves.<br /><br /><br />**9. Supersonic Flight Time:**<br /><br />* **Mach Number:** Mach number is the ratio of the object's speed to the speed of sound. Mach 2.2 means the plane is traveling at 2.2 times the speed of sound.<br /><br />* **Speed of Sound:** The speed of sound in air at 0°C is approximately 331 m/s.<br /><br />* **Plane's Speed:** Speed = Mach number * Speed of sound = 2.2 * 331 m/s = 728.2 m/s<br /><br />* **Distance:** 8.0 x 10³ km = 8.0 x 10⁶ m<br /><br />* **Time:** Time = Distance / Speed = (8.0 x 10⁶ m) / (728.2 m/s) = 11013.45 s ≈ 3.06 hours (approximately 3.1 hours)<br /><br /><br />**10. Standing Waves on a Spring:**<br /><br />* **a) Antinodes:** A standing wave with 5 nodes (including the fixed ends) will have 4 antinodes. The number of antinodes is always one less than the number of nodes.<br /><br />* **b) Wave Speed:**<br /><br /> * **Wavelength:** With 5 nodes on a 1.0 m spring, there are 2 full wavelengths. Therefore, the wavelength (λ) is 1.0 m / 2 = 0.5 m.<br /><br /> * **Speed:** Wave speed (v) is given by the formula v = fλ, where f is the frequency. v = (5.0 Hz)(0.5 m) = 2.5 m/s<br /><br /><br />**11. Resonant Length of Air Column:**<br /><br />* **Wavelength:** For the first resonance in a closed air column, the length of the air column is one-quarter of the wavelength (λ/4).<br /><br />* **Speed of Sound at 22°C:** The speed of sound in air increases with temperature. We can use the approximation v = 331 m/s + (0.6 m/s/°C) * T, where T is the temperature in Celsius. v = 331 m/s + (0.6 m/s/°C) * 22°C ≈ 344.2 m/s<br /><br />* **Wavelength:** v = fλ => λ = v/f = (344.2 m/s) / (128 Hz) ≈ 2.69 m<br /><br />* **Resonant Length:** Length = λ/4 = (2.69 m) / 4 ≈ 0.67 m<br />