Topic 1 Wave speed on strings.

(a)    State in words the following mathematical model

(b)   Describe qualitatively with two examples

Topic 2 Standing Waves

What are the boundary conditions for standing waves on a
(a)    string fixed at both ends?
(b)   pipe open at both ends?
(c)    pipe open at one end and closed at the other?

Topic 3 Loudness

(a) What is a decibel?

(c)    What is the intensity of the quietest sound the normal ear can hear?

(d)   What is the threshold of pain?

Examples

A piece of magician’s rope having a mass 91 g and a length 7.0 m is attached to a stand at one end and attached to a calibrated spring giving it a tension 2 N.
(a) What will be the speed of waves on the magic rope?
(b) What should be the tension such that there will be one node in the middle when shook?
(b) At what frequency should it be shook?

A flute acts like a pipe open at both ends, one end being the mouth hole and the other a finger hole. A clarinet on the other hand, acts like a pipe open at one end and closed at the other. Assuming he speed of sound is 347 m/s,  and the note of A4 has a frequency of 440 Hz, what should be the length between the mouth hole and the finger hole for the note A5 for (a) a flute and (b) a clarinet.

A cheerleader Calling the Hogs can, without hurting her voice, create a sound intensity of 10⁸ times greater than the threshold of human hearing, generally taken as 10^-12 W/m2.
(a) What is the decibel level of one cheerleader?
(b) What is the decibel level of ten cheerleaders?
(c) What is the decibel level of two cheerleaders?

Textbook Problems