Chapter 16 Wave Motion EXAMPLES

Chapter 16 Wave Motion: EXAMPLES

Example 16-1: 3D Earthquake Waves P waves “P” stands for primary Fastest, at 7 – 8 km / s Longitudinal S waves “S” stands for secondary Slower, at 4 – 5 km/s Transverse A seismograph records the waves and allows determination of information about the earthquake’s place of origin

Example 16-2: A Traveling Sinusoidal Wave The wavelength, λ= 40.0 cm, the amplitude, A = 15.0 cm, and a frequency f = 8.00 Hz Find: k, T,  and speed v of the wave k ≡ 2/λ = 2/40 cm = 0.157 rad/cm T = 1/f = 1/8.00s-1 = 0.125 s  =2f = 6.28rad(8.00s-1) = 50.3 rad/s v = λ f = 40cm(8.00s-1) = 320 cm/s The wave function can be written in the form y = A cos(kx – t)  y = (15.0cm) cos(0.157x – 50.3t)

Example 16-3: A Sinusoidal Driven String The string is driven at a frequency f = 5.00 Hz. The Amplitude of the motion is 12.0 cm and the wave speed v is 20.0 m/s Find: angular frequency  and wave number k  ≡ 2f = 6.28rad(5.00s-1) = 31.4 rad/s k ≡  /v = 31.4/20 rad/m = 1.57 rad/m The wave function can be written in the form y = A sin(kx – t)  y = (0.120m) sin(1.57x – 31.4t)

Example 16-4: The Speed of a Pulse on a Cord A uniform cord has a mass of 0.300kg and a length of 6.00 m. The cord passes over a pulley and supports a 2.00 kg object (see figure) Find the speed of a pulse traveling along the cord. The tension T in the cord is equal to the weight of the suspended object: T = mg = 2.00kg(9.60m/s2) = 19.6N (neglecting mass of the cord) The mass per unit length: μ = m/l = 0.300kg/6.00m = 0.050 kg/m  v = (T/μ)½ = (19.6N/0.050kg/m)½ = 19.8 m/s

Example 16-5: Power Supplied to a Vibrating String A taut string with µ = 5.00x10-2 kg/m is under tension T = 80.0 N How much power must be supplied to the string to generate sinusoidal waves at a frequency of 60.0 Hz and an amplitude of 6.00cm? First the wave speed on the string is: v = (T/m )½ = (80.0N/0.050kg/m)½ = 40.0 m/s The angular frequency will be:  ≡ 2f = 6.28rad(60.0s-1) = 377 rad/s  P = ½ µ ω2A2v P = ½(5.00x10-2 kg/m)(377 rad/s)2(0.06m)2(40.0m/s) P = 512W

Material from the book to Study!!! Material for the Midterm Material from the book to Study!!! Objective Questions: 4-6 Conceptual Questions: 4-6 Problems: 1-9-15-27-30-35-43-53