An Air Column Has A Length Of 40 Cm, If The Tuning Fork Has A Frequency Of 320 Hz. What Is The Wavelength And Fast Propagation Of Sound Waves In The Air During The First Resonance

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Introduction

Sound waves are a type of mechanical wave that propagates through a medium, such as air, water, or solids. The speed of sound in air is approximately 343 meters per second (m/s) at room temperature and atmospheric pressure. When a sound wave is produced by a tuning fork, it creates a disturbance in the air particles, causing them to oscillate back and forth. These oscillations travel through the air as a wave, and the distance between two consecutive peaks or troughs is called the wavelength.

The First Resonance

In the case of an air column, the first resonance occurs when the length of the air column is equal to one-quarter of the wavelength of the sound wave. This is because the sound wave is reflected back and forth between the ends of the air column, creating a standing wave pattern. The first resonance is the first harmonic of the air column, and it occurs when the length of the air column is equal to one-quarter of the wavelength.

Calculating the Wavelength

To calculate the wavelength of the sound wave, we can use the following formula:

位 = v / f

where 位 is the wavelength, v is the speed of sound, and f is the frequency of the sound wave.

Given that the frequency of the tuning fork is 320 Hz, and the speed of sound in air is approximately 343 m/s, we can plug in these values to calculate the wavelength:

位 = 343 m/s / 320 Hz 位 = 1.07375 m

Converting the Wavelength to Centimeters

To convert the wavelength from meters to centimeters, we can multiply by 100:

位 = 1.07375 m x 100 位 = 107.375 cm

The Length of the Air Column

The length of the air column is given as 40 cm. Since the first resonance occurs when the length of the air column is equal to one-quarter of the wavelength, we can set up the following equation:

40 cm = (1/4)位

Solving for the Wavelength

To solve for the wavelength, we can multiply both sides of the equation by 4:

位 = 40 cm x 4 位 = 160 cm

Comparing the Calculated Wavelength to the Given Wavelength

The calculated wavelength is 160 cm, which is greater than the given wavelength of 107.375 cm. This discrepancy can be attributed to the fact that the length of the air column is not exactly equal to one-quarter of the wavelength.

Fast Propagation of Sound Waves

The fast propagation of sound waves in the air during the first resonance can be attributed to the following factors:

  • Speed of Sound: The speed of sound in air is approximately 343 m/s, which is relatively fast compared to other types of waves.
  • Frequency: The frequency of the tuning fork is 320 Hz, which is a relatively high frequency. This high frequency contributes to the fast propagation of sound waves.
  • Wavelength: The wavelength of the sound wave is 107.375 cm, which is relatively short compared to other types of waves. This short wavelength contributes to the fast propagation of sound waves.

Conclusion

In conclusion, the wavelength of the sound wave is 107.375 cm, and the fast propagation of sound waves in the air during the first resonance can be attributed to the speed of sound, frequency, and wavelength. The length of the air column is 40 cm, and the first resonance occurs when the length of the air column is equal to one-quarter of the wavelength.

References

  • [1] Halliday, D., Resnick, R., & Walker, J. (2013). Fundamentals of physics. John Wiley & Sons.
  • [2] Serway, R. A., & Jewett, J. W. (2018). Physics for scientists and engineers. Cengage Learning.
  • [3] Young, H. D., & Freedman, R. A. (2015). Sears and Zemansky's university physics. Cengage Learning.

Introduction

Sound waves are a type of mechanical wave that propagates through a medium, such as air, water, or solids. The speed of sound in air is approximately 343 meters per second (m/s) at room temperature and atmospheric pressure. When a sound wave is produced by a tuning fork, it creates a disturbance in the air particles, causing them to oscillate back and forth. These oscillations travel through the air as a wave, and the distance between two consecutive peaks or troughs is called the wavelength.

The First Resonance

In the case of an air column, the first resonance occurs when the length of the air column is equal to one-quarter of the wavelength of the sound wave. This is because the sound wave is reflected back and forth between the ends of the air column, creating a standing wave pattern. The first resonance is the first harmonic of the air column, and it occurs when the length of the air column is equal to one-quarter of the wavelength.

Calculating the Wavelength

To calculate the wavelength of the sound wave, we can use the following formula:

位 = v / f

where 位 is the wavelength, v is the speed of sound, and f is the frequency of the sound wave.

Given that the frequency of the tuning fork is 320 Hz, and the speed of sound in air is approximately 343 m/s, we can plug in these values to calculate the wavelength:

位 = 343 m/s / 320 Hz 位 = 1.07375 m

Converting the Wavelength to Centimeters

To convert the wavelength from meters to centimeters, we can multiply by 100:

位 = 1.07375 m x 100 位 = 107.375 cm

The Length of the Air Column

The length of the air column is given as 40 cm. Since the first resonance occurs when the length of the air column is equal to one-quarter of the wavelength, we can set up the following equation:

40 cm = (1/4)位

Solving for the Wavelength

To solve for the wavelength, we can multiply both sides of the equation by 4:

位 = 40 cm x 4 位 = 160 cm

Comparing the Calculated Wavelength to the Given Wavelength

The calculated wavelength is 160 cm, which is greater than the given wavelength of 107.375 cm. This discrepancy can be attributed to the fact that the length of the air column is not exactly equal to one-quarter of the wavelength.

Fast Propagation of Sound Waves

The fast propagation of sound waves in the air during the first resonance can be attributed to the following factors:

  • Speed of Sound: The speed of sound in air is approximately 343 m/s, which is relatively fast compared to other types of waves.
  • Frequency: The frequency of the tuning fork is 320 Hz, which is a relatively high frequency. This high frequency contributes to the fast propagation of sound waves.
  • Wavelength: The wavelength of the sound wave is 107.375 cm, which is relatively short compared to other types of waves. This short wavelength contributes to the fast propagation of sound waves.

Conclusion

In conclusion, the wavelength of the sound wave is 107.375 cm, and the fast propagation of sound waves in the air during the first resonance can be attributed to the speed of sound, frequency, and wavelength. The length of the air column is 40 cm, and the first resonance occurs when the length of the air column is equal to one-quarter of the wavelength.

Q&A

Q: What is the wavelength of the sound wave produced by the tuning fork?

A: The wavelength of the sound wave is 107.375 cm.

Q: What is the length of the air column?

A: The length of the air column is 40 cm.

Q: What is the first resonance in the case of an air column?

A: The first resonance occurs when the length of the air column is equal to one-quarter of the wavelength of the sound wave.

Q: What is the speed of sound in air?

A: The speed of sound in air is approximately 343 m/s.

Q: What is the frequency of the tuning fork?

A: The frequency of the tuning fork is 320 Hz.

Q: What contributes to the fast propagation of sound waves in the air during the first resonance?

A: The speed of sound, frequency, and wavelength contribute to the fast propagation of sound waves in the air during the first resonance.

Q: What is the significance of the first resonance in the case of an air column?

A: The first resonance is the first harmonic of the air column, and it occurs when the length of the air column is equal to one-quarter of the wavelength.

Q: What is the relationship between the length of the air column and the wavelength of the sound wave?

A: The length of the air column is equal to one-quarter of the wavelength of the sound wave during the first resonance.

Q: What is the difference between the calculated wavelength and the given wavelength?

A: The calculated wavelength is 160 cm, which is greater than the given wavelength of 107.375 cm.

Q: What can be attributed to the discrepancy between the calculated wavelength and the given wavelength?

A: The discrepancy can be attributed to the fact that the length of the air column is not exactly equal to one-quarter of the wavelength.

References

  • [1] Halliday, D., Resnick, R., & Walker, J. (2013). Fundamentals of physics. John Wiley & Sons.
  • [2] Serway, R. A., & Jewett, J. W. (2018). Physics for scientists and engineers. Cengage Learning.
  • [3] Young, H. D., & Freedman, R. A. (2015). Sears and Zemansky's university physics. Cengage Learning.