the distance between a loudspeaker and the left ear of a listener is 2.70 m a) calculate the time required for sound to travel this distance if the air temperature is 20oC. b) assuming that the sound frequency is 523 Hz, how many wavelengths of sound are contained in this distance?
The speed of sound in an ideal gas is given by the relationship
• R = the universal gas constant = 8.314 J/mol K,
• T = the absolute temperature
• M = the molecular weight of the gas in kg/mol
• = the adiabatic constant, characteristic of the specific gas
For air, the adiabatic constant γ = 1.4 and the average molecular mass for dry air is 28.95 gm/mol. At T = 200C = 293.160C,
vsound = 343.32 m/s
Time = Distance/speed = 2.70/343.32 = 7.86 ms
b) Assuming that the sound frequency is 523 Hz, how many wavelengths of sound are contained in this distance?
v = n
Number of wavelnegths contained in 2.7 m =
To calculate the time required for sound to travel a distance, we can use the formula:
Time = Distance / Speed
a) The speed of sound in air at 20°C is approximately 343 meters per second. Using this information and the given distance of 2.70 meters, we can calculate the time required for sound to travel this distance.
Time = 2.70 m / 343 m/s
= 0.00787 seconds
Therefore, the time required for sound to travel this distance is approximately 0.00787 seconds.
b) To calculate the number of wavelengths of sound contained in the given distance, we need to know the speed of sound and the frequency of the sound wave.
The speed of sound in air is the same as in part a, which is 343 meters per second.
We're given the frequency of the sound wave as 523 Hz. The formula relating speed, frequency, and wavelength is:
Speed = Frequency × Wavelength
Rearranging the formula, we get:
Wavelength = Speed / Frequency
Wavelength = 343 m/s / 523 Hz
= 0.656 meters
So, the wavelength of the sound wave is 0.656 meters.
To find the number of wavelengths contained in the given distance, we divide the distance by the wavelength:
Number of wavelengths = Distance / Wavelength
= 2.70 m / 0.656 m
≈ 4.12 wavelengths
Therefore, approximately 4.12 wavelengths of sound are contained in a distance of 2.70 meters.