A wave of wavelength 0.6 cm is produced in air and it travels at a speed of 300 m/s. Will it be audible?

by

Points to Remember:

  • The audible range of human hearing is generally considered to be between 20 Hz and 20,000 Hz.
  • The relationship between wavelength (λ), frequency (f), and speed (v) of a wave is given by: v = fλ.
  • We need to calculate the frequency of the wave to determine if it falls within the audible range.

Introduction:

Sound is a longitudinal wave that travels through a medium, such as air. The human ear can detect sound waves within a specific frequency range. Sounds with frequencies below 20 Hz are called infrasound, and those above 20,000 Hz are called ultrasound; both are inaudible to humans. This question requires us to determine the frequency of a given sound wave and assess whether it lies within the audible range. The speed of sound in air at room temperature is approximately 343 m/s, but the question provides a speed of 300 m/s, which we will use for consistency.

Body:

1. Calculating the Frequency:

The question provides the wavelength (λ) as 0.6 cm, which is 0.006 m, and the speed (v) as 300 m/s. Using the formula v = fλ, we can calculate the frequency (f):

f = v / λ = 300 m/s / 0.006 m = 50,000 Hz

2. Assessing Audibility:

The calculated frequency of 50,000 Hz is significantly higher than the upper limit of the human audible range (20,000 Hz).

3. Conclusion:

The sound wave with a wavelength of 0.6 cm and a speed of 300 m/s has a frequency of 50,000 Hz. Since this frequency is above the upper limit of human hearing, the sound wave will not be audible to humans. It falls into the ultrasound range. This highlights the limitations of human perception and the existence of sound waves beyond our capacity to hear. Further research into ultrasound technology could explore its applications in various fields, such as medical imaging and non-destructive testing, emphasizing the importance of understanding the full spectrum of sound waves.

MPPCS  Notes brings Prelims and Mains programs for MPPCS  Prelims and MPPCS  Mains Exam preparation. Various Programs initiated by MPPCS  Notes are as follows:- For any doubt, Just leave us a Chat or Fill us a querry––