- #1

lizzyb

- 168

- 0

We have the equation: [tex]\Delta r = \frac{\phi}{2 \pi} \lambda[/tex] so it seems that all we need to do is determine phi since we can easily determine delta r and lambda. But the answer that I come up with is different than in the book.

[tex]\lambda = \frac{v}{f} = \frac{343}{246} = 1.39 m[/tex]

Easy enough. But what about the change in r? Let r1 be the distance traveled by the sound that goes to the left and r2 be the sound that goes to the right, thus we have:

[tex]r_1 = 2(47 - 14) = 66 m[/tex]

[tex]r_2 = 2(14) = 28 m[/tex]

[tex]\Delta r = r_1 - r2 = 38 = \frac{\phi}{2 \pi} \lambda[/tex]

so [tex]\frac{38 \cdot 2 \cdot \pi}{1.39} = \phi[/tex]

Which is 171.77 radians maybe? But this is way off the answer in the back of the book, 91.3 degrees, because 171.77 * 180 / pi = 9841.7 degrees modulo 360 = 121 degrees??

??