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When a 440-Hz tuning fork and a piano key are struck together, five beats are heard. If the pitch of the note on the piano is higher than the tuning fork, what is the frequency of the note?

440 Hz
445 Hz
435 Hz
435 or 445 Hz

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MissPhiladelphia
For the answer to the question above asking, what is the frequency of the note when a 440-Hz tuning fork and a piano key are struck together, five beats are heard. If the pitch of the note on the piano is higher than the tuning fork?
42/2 = 21Hz 2) 440-5 =
So the answer would be the third one among the given choices which is 435 Hz

Answer:

The frequency of the note is 435 Hz and 445 Hz.

(d) is correct option.

Explanation:

Given that,

Frequency of tuning fork= 440 Hz

Heard of beat = 5

We know that,

The difference between the frequencies of the note and the tuning fork gives the frequency of the beats.

[tex]f_{b}=f_{t}-f_{n}[/tex]...(I)

[tex]f_{b}=f_{n}-f_{t}[/tex]....(II)

Here, [tex]f_{b}[/tex] =beat number

[tex]f_{t}[/tex] = frequency of tuning fork

[tex]f_{n}[/tex] = frequency of note

Put the value in equation (I)

[tex]5= 440-f_{n}[/tex]

[tex]-f_{n}=-440+5[/tex]

[tex]f_{n}=435\ Hz[/tex]

Now, put the value of [tex]f_{b}[/tex] and [tex]f_{t}[/tex] in equation (II)

[tex]f_{b}=f_{n}-f_{t}[/tex]

[tex]5=f_{n}-440[/tex]

[tex]f_{n}=445\ Hz[/tex]

Hence, The frequency of the note is 435 Hz and 445 Hz.

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