The speed of a wave on a stretched string can be calculated from the tension, F,

Question

The speed of a wave on a stretched string can be calculated from the tension, F, and the linear mass density, m/L, by using the equation v = [F/(m/L)]^1/2 That is, the wave speed equals the square root of the tension divided by the linear mass density. If the uncertainty in the tension is 4% and the uncertainty in the linear mass density is 2%, what is the uncertainty in the calculated wave speed? 6% 8% 3% 4% Suppose you have a string that is being made to vibrate at a specific frequency, f. The speed of waves on the string is v. The length of the string that is vibrating, L, is adjustable. When the length of the string has been adjusted so that the fundamental standing wave pattern forms, write the expression for L in terms of f and v. (The fundamental standing wave pattern corresponds to nodes at each end of the string and an antinode in the middle.) A stretched string is attached to an oscillator. On which of the following quantities does the wavelength of the waves on the string depend? Select all that apply. The linear mass density of the string. The frequency of the oscillator. The tension applied to the string. The amplitude of the oscillator's motion.

Explanation / Answer

1) v = sqrt[F/p] where p = m/l =mass density

ln v = 0.5[lnF - lnp]

dv/v = 0.5[dF/F + dp/p] = 0.5[0.04 + 0.02]

dv/v = 0.03 = 3%   

2) As wavelength = 2L

Also wavelength = v/f = 2L

So, L =v/2f

3)   We know that v = sqrt[F/p]

Also v = wavelength*f

from both, sqrt[F/p] = wavelength*f

  wavelength = (1/f)*sqrt[F/p]

Thus  wavelength depends on frequency, tension and linear mass density.

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