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b. a guitar string has a length of 0.90 m. when you pluck it, it plays a “c” that has a frequency of 256 hz. how fast is the wave moving back and forth along the string? (choose one of the equations from the box at the top of the page to solve this problem.)
c. in a train track made of solid steel, sound waves travel extremely fast – about 6,000 m/s. if a train’s vibration travels for 3 seconds, how far will it move? (choose one of the equations from the box at the top of the page to solve this problem.)

ANSWER:

b. 460.8 m/s

c. 18,000 m

EXPLANATION:

[i] We have a stringth with length L = 0.90 m, and a standing wave with frequency f = 256 Hz. The equation that relates the speed of the wave with the frequency and the length of the string is

where v is the speed of the wave. Re-arranging the equation and putting in the numbers, we find:

[ii] The speed of the sound wave in steel is v = 6000 m/s. The train's vibration travels for 3 seconds, so the distance covered by the sound wave during this time can be calculated using the formula

Re-arranging the equation and substituting the numbers, we can find d:

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