1. The speed of a sound wave is 340 m/s and its wavelength is 34 m. Is it audible to human beings? Justify your answer.
2. Wavelength of a sound having a frequency 2 kHz is 35 cm. How much time will it take to travel 100 m?
3. Limit of audibility to human beings is 20 Hz to 20000 Hz. If so, what will be the limit of a wavelength of sound waves that are audible to human beings? (Speed of sound in air = 340 m/s)
Answer (2)
The sound wave at 10 Hz is not audible to humans, as it is below the 20 Hz threshold. It takes about 0.294 seconds for a sound wave at 2 kHz to travel 100 m. The audible wavelength range for humans is approximately from 0.017 m (1.7 cm) to 17 m based on the frequency limits of 20 Hz to 20000 Hz.
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Is the sound wave audible to human beings?
The speed of the sound wave is given as 340 m/s and its wavelength is 34 m . We can find the frequency using the formula: f = λ v where f is frequency, v is speed, and λ is wavelength.
f = 34 340 = 10 Hz
The frequency of the sound is 10 Hz , which is below the audible range for humans (20 Hz to 20,000 Hz). Therefore, this sound is not audible to human beings.
Time to travel 100 m for a sound wave of frequency 2 kHz with wavelength 35 cm.
First, convert the wavelength from centimeters to meters: 35 cm = 0.35 m .
Given the frequency f = 2000 Hz (since 1 kHz = 1000 Hz), and the speed of sound v = 340 m/s , we can check the wavelength consistency using the formula: λ = f v
λ = 2000 340 = 0.17 m
The given wavelength 0.35 m does not match. However, let's find the time to travel 100 m using the speed given (assuming speed is correct):
Time = Speed Distance = 340 100 ≈ 0.294 seconds
Limit of wavelength audible to human beings:
The limit of audibility for humans is 20 Hz to 20,000 Hz. We can find the wavelength limits using the formula for speed of sound v = 340 m/s .
- For the lower frequency (20 Hz):
λ max = f min v = 20 340 = 17 m
- For the higher frequency (20,000 Hz):
λ min = f max v = 20 , 000 340 = 0.017 m
Thus, the limit of the wavelength of sound waves audible to humans ranges from 0.017 m (17 mm) to 17 m .
