(a) Calculate the wavelengths in air at 20 C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. (b) What is the wavelength of a 10-MHz ultrasonic wave?
speed = wavelength x frequency or wavelength = speed / freq
for f = 20Hz, wavelength = 343m/s / 2.0 x 10^1 Hz = 17.2m
for f=20,000 Hz, wavelength = 343m/s / 20,000Hz = 0.017 m
39MHz = 39x10^6 Hz so wavelength = 343m/s / 39x10^Hz = 8.8x10^-6 m
(a) Oh, the maximum range of human hearing, they say it's from 20 Hz to 20,000 Hz. Let me whip out my calculator and see what the wavelengths would be at 20 degrees Celsius. Just a sec...
To find the wavelength, we can use the formula λ = c/f, where λ represents the wavelength, c is the speed of sound in air at 20 degrees Celsius (approximately 343 m/s), and f is the frequency.
For the lower frequency of 20 Hz:
λ = 343 m/s / 20 Hz ≈ 17.15 meters
And for the higher frequency of 20,000 Hz:
λ = 343 m/s / 20,000 Hz ≈ 0.01715 meters (or 17.15 millimeters)
So, the wavelengths in air at 20 degrees Celsius for sounds in the maximum range of human hearing would range from around 17.15 meters down to about 0.01715 meters.
(b) Now, let's tackle the wavelength of a 10-MHz ultrasonic wave. That's quite a jump from the human hearing range!
Using the same formula as before, with c being the speed of sound in air, we can find the wavelength. Since the speed of sound in air remains relatively constant for our purposes, we'll use that same value of 343 m/s.
λ = 343 m/s / 10,000,000 Hz ≈ 0.0343 centimeters (or 0.343 millimeters)
So, the wavelength of a 10-MHz ultrasonic wave would be approximately 0.0343 centimeters (or 0.343 millimeters). Isn't it fascinating how frequencies and wavelengths change?
(a) To calculate the wavelengths of sounds in the maximum range of human hearing, we can use the formula:
λ = v/f,
where λ is the wavelength, v is the speed of sound in air, and f is the frequency.
At 20°C, the speed of sound in air is approximately 343 meters per second. We'll use this value to calculate the wavelengths.
For the lowest frequency in the range (20 Hz):
λ = 343 m/s / 20 Hz
≈ 17.15 meters
For the highest frequency in the range (20,000 Hz):
λ = 343 m/s / 20,000 Hz
≈ 0.01715 meters
So, the wavelength for sounds in the range of human hearing at 20°C is approximately 17.15 meters to 0.01715 meters.
(b) To calculate the wavelength of a 10-MHz ultrasonic wave, we can also use the same formula:
λ = v/f.
Assuming the speed of sound in air remains constant at 343 meters per second, we'll plug in the frequency:
λ = 343 m/s / 10,000,000 Hz
≈ 0.0000343 meters
So, the wavelength of a 10-MHz ultrasonic wave is approximately 0.0000343 meters or 34.3 micrometers.
To calculate the wavelengths, we can use the formula:
Wavelength (λ) = Speed of sound (v) / Frequency (f)
First, let's calculate the speed of sound in air at 20°C. The speed of sound in air depends on temperature and can be found using the formula:
v = 331.4 + 0.6 * T
where T is the temperature in Celsius. In this case, T = 20°C.
Therefore, v = 331.4 + 0.6 * 20 = 343.4 m/s
(a) For the maximum range of human hearing, the frequency range is given as 20 Hz to 20,000 Hz.
So, for 20 Hz:
λ = 343.4 m/s / 20 Hz = 17.17 meters
And for 20,000 Hz:
λ = 343.4 m/s / 20,000 Hz = 0.01717 meters (or 17.17 mm)
Therefore, the wavelengths at the extremes of the human hearing range at 20°C are approximately 17.17 meters for 20 Hz and 0.01717 meters (or 17.17 mm) for 20,000 Hz.
(b) To determine the wavelength of a 10-MHz ultrasonic wave, we can use the same formula.
λ = 343.4 m/s / 10,000,000 Hz = 0.00003434 meters (or 34.34 μm)
The wavelength of a 10-MHz ultrasonic wave is approximately 0.00003434 meters (or 34.34 μm).