Question

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

Answer 1

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

Step-by-step 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
`f_b` will be;

`f_b` = 1 / T

we substitute in the value of T

`f_b` = 1 / 0.28

`f_b` = 3.5714 Hz

Now, we know that;
`f_b` =
`f_2` -
`f_1`

we solve for
`f_2`

`f_2` =
`f_b` +
`f_1`

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

we substitute

`f_2` = 3.5714 Hz + 173.5 Hz

`f_2` = 177.07 Hz

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