Question
A Question 6 (1 point) Retake question 4) Listen The following wave function represents a travelling wave: y(x,t)=(7.8)/(8.7+(6.3x+5.6t)^2) What is the phase velocity? Your Answer: square square Answer units
Solution
4.7
(194 Votes)
Juliette
Elite · Tutor for 8 years
Answer
The wave function is given by:y(x,t) = 7.8 / (8.7 + (6.3x + 5.6t)^2)This represents a wave traveling in the negative x-direction. The general form for such a wave is:y(x,t) = f(kx + ωt) where the phase velocity, v, is given by v = -ω/kIn our case, we can rewrite the argument within the parenthesis as:6.3x + 5.6t = 6.3(x + (5.6/6.3)t)Comparing this to kx + ωt, we can identify:k = 6.3ω = 5.6Therefore, the phase velocity is:v = -ω/k = -5.6/6.3 = -0.8888...So, the phase velocity is approximately **-0.89** units (presumably m/s or cm/s depending on the units of x and t, which aren't specified).