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lizzyb
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A tuning fork generates sound waves with a frequency of 246 Hz. The waves travel in opposite directions along a hallway, are reflected by end walls, and return. The hallway is 47.0 m long, and the tuning fork is located 14.0 m from one end. What is the phase difference between the reflected waves when they meet at the tuning fork? The speed of sound in air is 343 m/s.
We have the equation: \Delta r = \frac{\phi}{2 \pi} \lambda 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.
\lambda = \frac{v}{f} = \frac{343}{246} = 1.39 m
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:
r_1 = 2(47 - 14) = 66 m
r_2 = 2(14) = 28 m
\Delta r = r_1 - r2 = 38 = \frac{\phi}{2 \pi} \lambda
so \frac{38 \cdot 2 \cdot \pi}{1.39} = \phi
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??
??
We have the equation: \Delta r = \frac{\phi}{2 \pi} \lambda 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.
\lambda = \frac{v}{f} = \frac{343}{246} = 1.39 m
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:
r_1 = 2(47 - 14) = 66 m
r_2 = 2(14) = 28 m
\Delta r = r_1 - r2 = 38 = \frac{\phi}{2 \pi} \lambda
so \frac{38 \cdot 2 \cdot \pi}{1.39} = \phi
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??
??