Chapter 10 & 11

Elasticity, Oscillations,

Waves, and Sound

 

Mechanical Waves

A progressive or traveling wave is a self-sustaining disturbance of a medium that propagates from one region to another, carrying energy and momentum.

 

Longitudinal Wave – the sustaining medium is displaced parallel to the direction of propagation.

 

Transverse Wave – the sustaining medium is displaced perpendicular to the direction of propagation.

 

 

Period – the time it takes for a wave to go through one complete oscillation.

Frequency – the number of complete oscillations the wave makes in a second.

Wavelength – the spatial distance over which the wave makes one complete oscillation.

 

Speed of any progressive periodic wave:

(16)

 

Problem 16

Sound waves travel in air with a speed of 343 m/s. The lowest frequency sound we can hear is 20.0 Hz; the highest frequency is 20.0 kHz. Find the wavelength of sound for frequencies of 20.0 Hz and 20.0 kHz.

 

Solution:

Solve equation (16) for the wavelength:

 

Transverse Waves: Strings

Speed of a transverse wave in a string:

(17)

where is the tension in the string and m/L is the mass per unit length.

 

Example 17

A 5.0 m length of rope, with a mass of 0.52 kg, is pulled taut with a tension of 46 N. Find the speed of waves on the rope.

 

Solution:

Use equation (17) to find the speed of the wave:

 

Example 18

A 12 m rope is pulled tight with a tension of 92 N. When one end of the rope is given a "thunk" it takes 0.45 s for the disturbance to propagate to the other end. What is the mass of the rope?

 

Solution:

Calculate the speed of the wave:

Use equation (17) to solve for the mass:

Sound Part 2