The lower frequency limit for human hearing is usually considered to be 20.0 Hz. (a) What is

the speed of sound in m/s if the air temperature is 20.0ºC? (b) What is the corresponding
wavelength for this frequency?

a. V = 343 m/s.

b. L = V/F = 343/20 = 17.15 m.

(a) The speed of sound is approximately 343 m/s at 20ºC, but let's use a little humor to calculate that. On a sunny day, speed is running late for an important meeting when it sees a sign that says "Speed Limit = The Speed of Sound." Curious, it checks its watch and realizes it's going to be late, so it starts running at full speed, hoping to catch up with the sound. After a while, it finally catches up, huffing and puffing, and asks the sound, "Hey, how fast were you going?" The sound, confident as ever, replies, "Oh, I was going at a cool 343 meters per second!" So, the speed of sound at 20ºC is approximately 343 m/s.

(b) Now, for the corresponding wavelength, things get a bit tricky. The wavelength is like a shoelace, long and wavy. For the frequency of 20 Hz, let's imagine that the sound has a special dance move called the "Sound Wave Shuffle." It shuffles its feet back and forth 20 times per second, creating 20 peaks and 20 valleys in its wavelength. To find the corresponding wavelength, we need to divide the speed of sound by the frequency. So, we have:

343 m/s / 20 Hz = 17.15 meters

Therefore, the corresponding wavelength for a frequency of 20.0 Hz is approximately 17.15 meters. Keep grooving with those sound waves!

To determine the speed of sound in m/s at a temperature of 20.0ºC, we can use the formula:

v = 331.4 + 0.6 * T

Where:
v is the speed of sound in m/s
T is the air temperature in ºC

(a) Substituting the given temperature into the formula, we have:

v = 331.4 + 0.6 * 20.0
v = 331.4 + 12.0
v = 343.4 m/s

Therefore, the speed of sound at a temperature of 20.0ºC is 343.4 m/s.

(b) The wavelength (λ) can be calculated using the formula:

λ = v / f

Where:
λ is the wavelength
v is the speed of sound in m/s
f is the frequency in Hz

Given that the lower frequency limit for human hearing is 20.0 Hz, we can substitute the values into the formula to find the wavelength:

λ = 343.4 / 20.0
λ = 17.17 m

Therefore, the corresponding wavelength for a frequency of 20.0 Hz is 17.17 m.

To answer these questions, we need to make use of the formula relating the speed of sound, wavelength, and frequency. The formula is as follows:

Speed of sound = wavelength x frequency

(a) To determine the speed of sound, we need the wavelength and frequency. However, we are only given the frequency limit, which is 20.0 Hz. In order to proceed, we need additional information such as the wavelength or any other relevant data like the relationship between wavelength and frequency.

(b) To find the corresponding wavelength for a given frequency, we use the formula:

Wavelength = Speed of sound / Frequency

At this point, we are missing either the speed of sound or the frequency. Without this information, we cannot calculate the corresponding wavelength. Could you provide any other related data or clarify the question further so that we can proceed with the calculations?