Final answer:
The wavelength of a 4700 Hz longitudinal wave traveling along an iron rod is determined by calculating the speed of sound in iron using the elastic modulus and density, and then using the wave equation. The calculated wavelength is approximately 1.207 meters.
Step-by-step explanation:
To determine the wavelength of a 4700 Hz longitudinal wave traveling along an iron rod, we need to calculate the speed of sound in iron and then use the wave equation. The speed of sound in a solid can be calculated using the formula v = √(E/ρ), where E is the elastic modulus, and ρ is the density. The elastic modulus of iron is given as 100 × 109 N/m2, and the density is 7.8 × 103 kg/m3.
First, calculate the speed of sound in iron:
v = √(E/ρ) = √(100 × 109 N/m2 / 7.8 × 103 kg/m3)
v ≈ 5,674.15 m/s
Next, use the wave equation λ = v/f to find the wavelength, where λ is the wavelength, v is the speed of sound, and f is the frequency of the wave:
λ = 5,674.15 m/s / 4700 Hz ≈ 1.207 m
Therefore, the wavelength of a 4700 Hz wave traveling through iron is approximately 1.207 meters.