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" (that is, at too low a frequency). Playing at the same time as the first flute, she hears one loud-soft-loud beat per second. What is the frequency of her instrument?

Answer 1

Answer:

439 Hz

Explanation:

$f_1$ = Frequency of first wave = 440 Hz

F = Beat frequency = 1 Hz

$f_2$ = Frequency of the instrument

The beat frequency is the difference of the two waves which are interacting with each other

$F=f_1-f_2\\\Rightarrow 1=440-f_2\\\Rightarrow f_2=440-1\\\Rightarrow f_2=439\ Hz$

The frequency of the instrument is 439 Hz

Answer 2

When two sound waves having different values of their frequencies, approaches to ears, then the difference of these two frequency is known as beat frequency.

The beat frequency of the second player is 438 Hz.

What is beat frequency?

When two sound waves having different values of their frequencies, approaches to ears, then the difference of these two frequency is known as beat frequency. It can be given as,

$f_{beat}=f_A-f_B$

Given information-

One flute is properly tuned and plays the musical note A at exactly 440 Hz.

Suppose the frequency of the second player is $f$ Hz.

Let consider the beat frequency for the 2 waves is 2.Thus the beat frequency formula can be written as,

$2=440-f_B\\f_B=440-2\\f_B=438\rm Hz$

Thus the beat frequency of the second player is 438 Hz.

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