{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

wave_problems

# wave_problems - 1 Problems 15.27 15.37 15.41 15.79(1...

This preview shows pages 1–2. Sign up to view the full content.

1 Problems . 15 . 27 , 15 . 37 , 15 . 41 , 15 . 79 (1) 1. ( Estimates ) Estimate the mass per length of a double bass string. The lowest note on the bass is an E 1, ringing in at a cool 41 Hz just above human hearing. Based on the picture below, estimate the wavelength of this fundamental mode, and the velocity of a wave in the double bass string. Estimate the tension in the double bass low E string – give your answer in pounds and newtons. 2. ( Sinusoidal averages ) We have argued that sin 2 ( kx - ωt ) = 1 2 using the fact that sin 2 + cos 2 = 1. Here we would like to show result this more directly. The average of sin 2 and cos 2 over a period T is sin 2 2 πt T 1 T Z T 0 d t sin 2 2 πt T (2) cos 2 2 πt T 1 T Z T 0 d t cos 2 2 πt T (3) These integrals are computed by using the identity sin 2 ( x ) = 1 2 - 1 2 cos(2 x ) (4) cos 2 ( x ) = 1 2 + 1 2 cos(2 x ) (5) (a) Draw a graph of sin 2 ( x ) and cos 2 ( x ) and give a graphical explanation of the indentities given in Eq. 4 and Eq. 5. (b) Use these triginometic identities given to perform the integrals in Eq. 2 and Eq. 3 and show the result sin 2 = cos 2 = 1 2 3. ( Power )

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.

{[ snackBarMessage ]}