{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

mPhys390-hw1-sol

# mPhys390-hw1-sol - Physics 390 Homework set#1 Solutions...

This preview shows pages 1–3. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: January 17, 2007 Physics 390: Homework set #1 Solutions Reading: Tipler & Llewellyn, Chapter 3 Questions: 1. Show that the classical wave equation ∂ 2 f ∂t 2- c 2 ∂ 2 f ∂x 2 = 0 is satisfied by any function f that depends on x and t in the combination u = x ± ct : f ( x, t ) = f ( u ) = f ( x ± ct ). Solution: To see this, plug into the equation above: ∂ ∂t f = ∂f ∂u ∂u ∂t = ∂f ∂u ( ± c ) ∂ 2 ∂t 2 f = ∂ ∂t parenleftbigg ∂f ∂t parenrightbigg = ∂ ∂t bracketleftbigg ∂f ∂u ( ± c ) bracketrightbigg = ( ± c ) ∂ ∂t ∂f ∂u = ( ± c ) ∂ ∂u ∂f ∂u ∂u ∂t = ( ± c ) ∂ 2 f ∂u 2 ( ± c ) = c 2 ∂ 2 f ∂u 2 similarly, ∂ 2 f ∂x 2 = ∂ 2 f ∂u 2 parenleftbigg ∂u ∂x parenrightbigg 2 = ∂ 2 f ∂u 2 (1) = ∂ 2 f ∂u 2 and, ∂ 2 f ∂t 2- c 2 ∂ 2 f ∂x 2 = c 2 ∂ 2 f ∂u 2- c 2 ∂ 2 f ∂u 2 = 0 identically! 2. Planck’s constant is h = 6 . 626 × 10 − 34 J · s. What familiar physical quantity from classical me- chanics also has dimensions of J · s? Solution: Angular momentum also has dimensions of J · s. We will see that Planck’s constant is closely related to quantization of angular momentum. 1 3. In what region of the electromagnetic spectrum does the blackbody radiation from a roomtem- perature object peak? What sorts of problems would we have if our eyes were sensitive in this region? Solution: Room temperature is about 290 K. Using the Wien displacement law, we have λ max = 2 . 898 × 10 − 3 m · K 290 K = 1 × 10 − 5 m ....
View Full Document

{[ snackBarMessage ]}

### Page1 / 5

mPhys390-hw1-sol - Physics 390 Homework set#1 Solutions...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online