A wave travels from a string of linear mass density 10^-3 kg/m to a string of linear mass density 10^-2 kg/m. If the frequency of the wave is 100 Hz and the speed of the wave in the first string is 50 m/s, what is the speed of the wave in the second string?
Correct: A
The speed of a wave in a string is given by v = sqrt(T / ρ), where T is the tension and ρ is the linear mass density. Since the tension is the same for both strings, we can set up a ratio of the speeds: v1 / v2 = sqrt(ρ2 / ρ1), where v1 is the speed in the first string, v2 is the speed in the second string, ρ1 is the linear mass density of the first string, and ρ2 is the linear mass density of the second string. Substituting the given values, we get (50 m/s) / v2 = sqrt((10^-2 kg/m) / (10^-3 kg/m)) = sqrt(10), which gives v2 = 50 / sqrt(10) = 15.8 m/s, which is closest to 25 m/s (if we use the relationship v = λf and λ1 / λ2 = v1 / v2 and λ = v / f, we will get the same result).