Vibrations from a 650 Hz tuning fork sets up standing waves in a string clamped at both ends. The wave speed for the string is 410 m/s. The standing wave has four loops and an amplitude of 4.0 mm.
Incomplete.
To find the wavelength of the standing wave, we can make use of the information provided.
The number of loops in the standing wave represents the number of half-wavelengths present in the string. In this case, we are told that there are four loops. As one complete wave consists of two half-wavelengths, the number of loops is equal to the number of half-wavelengths, which implies that there are eight half-wavelengths in the string.
Since the standing wave is created by the vibrations of a tuning fork with a frequency of 650 Hz, the frequency of the standing wave is also 650 Hz. The frequency (f) of a wave is related to its wave speed (v) and wavelength (λ) by the equation:
v = fλ
In this case, the wave speed (v) is given as 410 m/s, and we need to find the wavelength (λ).
To find the wavelength, we can rearrange the equation:
λ = v/f
Substituting in the given values:
λ = 410 m/s / 650 Hz
Calculating this expression will give us the wavelength of the standing wave.