Question

A string with a linear mass density of 0.001 kg/m carries a tension of 0.4 N. A 100 Hz sinusoidal wave on this string has a wavelength of:

1. 20 cm
2. 500 cm
3. 2 cm
4. 2000 cm
5. 0.05 cm

Answer 1

To find the wavelength of the sinusoidal wave, first calculate the wave speed using the square root of the tension divided by the linear mass density, then divide that speed by the frequency of the wave. The wavelength for a 100 Hz wave under the given conditions is 20 cm.

Step-by-step explanation:

The question is asking for the wavelength of a sinusoidal wave that is traveling along a string with a given linear mass density and under a certain tension frequency. We can use the wave speed formula v = √(T/μ), where v is the speed of the wave, T is the tension, and μ is the linear mass density. Then, we use the formula v = f λ to find the wavelength λ, where f is the frequency of the wave.

First, we calculate the wave speed:

Wave speed, v = √(0.4 N / 0.001 kg/m) = √(400 m²/s²) = 20 m/s

Now, we can find the wavelength using the frequency of 100 Hz:

Wavelength, λ = v / f = 20 m/s / 100 Hz = 0.20 m or 20 cm

Therefore, the wavelength of the 100 Hz sinusoidal wave is 20 cm.