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Two ship fog horns have different frequencies. They are both being blown at the same time. You hear a sound that varies in amplitude, with the time between a minimum in loudness and the next maximum in loudness being 0.14 seconds. You know the fog horn with the lower pitch has a frequency of 173.5 Hz. What is the frequency of the fog horn with a higher pitch

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Nuhulawal20idn

Answer:

the frequency of the fog horn with a higher pitch is 177.07 Hz

Explanation:

Given the data in the question;

time between a minimum and the next maximum in loudness = 0.14 seconds

So,

Time T between the two continuous maximum in loudness will be;

⇒ T = 2 × 0.14 sec

T = 0.28 seconds

Thus, beat frequency [tex]f_b[/tex] will be;

[tex]f_b[/tex] = 1 / T

we substitute in the value of T

[tex]f_b[/tex] = 1 / 0.28

[tex]f_b[/tex]  = 3.5714 Hz

Now, we know that;  [tex]f_b[/tex] = [tex]f_2[/tex] - [tex]f_1[/tex]

we solve for [tex]f_2[/tex]

[tex]f_2[/tex] = [tex]f_b[/tex] + [tex]f_1[/tex]

given that; the lower pitch has a frequency of 173.5 Hz

we substitute

[tex]f_2[/tex] = 3.5714 Hz + 173.5 Hz

[tex]f_2[/tex] = 177.07 Hz

Therefore, the frequency of the fog horn with a higher pitch is 177.07 Hz

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