Brodie Beck

2022-10-06

Two ultrasonic sound waves combine and form a beat frequency that is in the range of human hearing. The frequency of one of the ultrasonic waves is 70 kHz. What is (a) the smallest possible and (b) the largest possible value for the frequency of the other ultrasonic wave?

### Answer & Explanation

The range of frequency that can be heard by human ear is from 20 Hz to 20 kHz.
The beat frequency is the frequency difference of two ultrasonic waves.
Frequency of one ultrasonic wave is given as 70 kHz and let f is the frequency of other ultrasonic wave.
(a) The smallest possible value of f can be found by taking the beat frequency equal to the smallest frequency that can be heard by human ears. That is,
$70000-f=20⇒f=70000-20=69080Hz=69.08kHz$
(Note: If we take f-70kHz = 20Hz, then we would get f=70.02kHz which is not smallest possible frequency.)
(b) To find the largest value that f can take, let us consider the beat frequency is equal to 20 kHz (the largest possible frequency that human ears can hear).
So we have
f-70kHz=20kHz (or)
f=(20+70)kHz=90kHz
Result:
(a)69.08kHz
(b)90kHz

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