Two ultrasonic sound waves combine and form a beat frequency that is in the range of human hearing for a healthy young person. The frequency of one of the ultrasonic waves is 84 kHz. (The range of hearing for a healthy young person is 20 Hz to 20 kHz.)
(a) What is the smallest possible value for the frequency of the other ultrasonic wave?
(b) What is the largest possible value for the frequency of the other ultrasonic wave?
84-20=64 smallest
84+20=104 largest
To find the smallest and largest possible values for the frequency of the other ultrasonic wave, we need to consider the beat frequency that falls within the range of human hearing.
(a) The beat frequency is the difference between the frequencies of the two ultrasonic waves. In this case, the beat frequency must be in the range of human hearing, which is 20 Hz to 20 kHz. Given that one of the ultrasonic waves has a frequency of 84 kHz, we can calculate the smallest possible value for the frequency of the other ultrasonic wave as follows:
Smallest beat frequency = 20 Hz
Frequency of the other ultrasonic wave = Frequency of the given wave - Smallest beat frequency
Frequency of the other ultrasonic wave = 84 kHz - 20 Hz = 83.99998 kHz
Therefore, the smallest possible value for the frequency of the other ultrasonic wave is approximately 83.99998 kHz.
(b) The largest beat frequency is 20 kHz, which is the upper limit of human hearing. Therefore, the largest possible value for the frequency of the other ultrasonic wave is obtained by subtracting the largest beat frequency from the frequency of the given wave:
Largest beat frequency = 20 kHz
Frequency of the other ultrasonic wave = Frequency of the given wave - Largest beat frequency
Frequency of the other ultrasonic wave = 84 kHz - 20 kHz = 64 kHz
Therefore, the largest possible value for the frequency of the other ultrasonic wave is 64 kHz.
To find the answers to these questions, we need to understand the concept of beat frequency.
When two waves interfere, they can combine to form an effect known as the beat frequency. This is the difference between the frequencies of the two waves. If the beat frequency falls within the range of human hearing (20 Hz to 20 kHz), it can be detected by a healthy young person.
Let's solve the questions step by step:
(a) What is the smallest possible value for the frequency of the other ultrasonic wave?
To find the smallest possible value, we need to subtract the maximum value of the beat frequency (20 kHz) from the given frequency (84 kHz):
Smallest possible frequency = 84 kHz - 20 kHz = 64 kHz.
So, the smallest possible value for the frequency of the other ultrasonic wave is 64 kHz.
(b) What is the largest possible value for the frequency of the other ultrasonic wave?
To find the largest possible value, we need to subtract the minimum value of the beat frequency (20 Hz) from the given frequency (84 kHz):
Largest possible frequency = 84 kHz - 20 Hz = 84 kHz.
So, the largest possible value for the frequency of the other ultrasonic wave is 84 kHz.
In summary:
(a) The smallest possible value for the frequency of the other ultrasonic wave is 64 kHz.
(b) The largest possible value for the frequency of the other ultrasonic wave is 84 kHz.