1. Chapter 16
Wave Motion EXAMPLES

2. Chapter 16 Wave Motion: EXAMPLES

3. 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

4. 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 = rad/cm
T = 1/f = 1/8.00s-1 = 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)

5. 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)

6. 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 = kg/6.00m = kg/m 
v = (T/μ)½ = (19.6N/0.050kg/m)½ = 19.8 m/s

7. 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

8. 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: