Question:

A sound wave travels through air, producing compressions and rarefactions. The speed of sound in air at room temperature is approximately 343 m/s. A tuning fork with a frequency of 440 Hz is struck and creates a sound wave.

a) Calculate the wavelength of this sound wave.

b) If the tuning fork is struck again and the frequency is doubled, what will be the new wavelength of the sound wave?

c) Calculate the period of the original sound wave produced by the tuning fork.

d) Determine the amplitude of the sound wave if it has an intensity of 0.04 W/m² at a distance of 2.0 meters from the source.

e) State one practical application of sound waves in everyday life.

Answer:

a) The speed of sound in air is given as 343 m/s and the frequency of the tuning fork is 440 Hz. We can use the formula for the speed of a wave to calculate the wavelength:

v = λ * f

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

Rearranging the equation to solve for wavelength:

λ = v / f

Substituting the given values:

λ = 343 m/s / 440 Hz = 0.78 m

Therefore, the wavelength of this sound wave is 0.78 m.

b) If the tuning fork's frequency is doubled to 2 * 440 Hz = 880 Hz, we can calculate the new wavelength using the same formula:

λ' = v / f'

Substituting the given values:

λ' = 343 m/s / 880 Hz = 0.39 m

Therefore, the new wavelength of the sound wave would be 0.39 m.

c) The period of a wave is the reciprocal of its frequency, so we can find the period using the formula:

T = 1 / f

Substituting the given frequency value:

T = 1 / 440 Hz ≈ 0.0023 s

Therefore, the period of the original sound wave is approximately 0.0023 seconds.

d) The intensity of a sound wave is related to its amplitude squared according to the formula:

I = A² * ρ * v

where I is the intensity, A is the amplitude, ρ is the density of the medium (in this case, air), and v is the speed of sound.

Rearranging the formula to solve for amplitude:

A = sqrt(I / (ρ * v))

Substituting the given values:

A = sqrt(0.04 W/m² / (1.2 kg/m³ * 343 m/s)) ≈ 0.009 m

Therefore, the amplitude of the sound wave is approximately 0.009 meters.

e) One practical application of sound waves in everyday life is through the use of ultrasound imaging. Ultrasound waves are used in medical imaging to create images of internal body structures. This technology is commonly used during pregnancy to monitor the development and health of the fetus.