Musicians can use beats to tune their instruments. One flute is properly tuned a

Question

Musicians can use beats to tune their instruments. One flute is properly tuned and plays the musical note A at exactly 440 Hz. A second player sounds the same note and hears that her instrument is slightly "flat" (i.e., at too low a frequency). Playing at the same time as the first flute, she hears one loud-soft-loud beat per second.

By how much she must shorten her flute to bring it into tune? Assume a speed of sound of 350 m/s.

Express your answer to two significant figures and include the appropriate units.

Explanation / Answer

Given that,

f1 = 440 Hz ; beat frequnecy = 3 beats per second.

beat frequency = f1 + f2

f2 = f1 - beat frequnecy = 440 - 3 = 437 Hz

we know that, f = v / 2L

f1 = v / 2L1

L1 = v / 2 f1 = 350 / 2 x 440 = 0.39772 m

L2 = v / 2 f2 = 350 / 2 x 437 = 0.40045 m

she need to shorten the flute by L = L2 - L1 = 0.40045 - 0.39772 = 0.0027 m.

Hence, L = 0.0027m = 2.7 x 10-3 m.

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