Question

Use the wave equation to find the speed of a wave given by y(x,t)=(3.00mm)sin[(4.00m −1 )x−(7.00s −1 )t].

a) 7.00m/s
b) 4.00m/s
c) 3.00mm/s
d) 0.57m/s

Answer 1

The wave speed is calculated as 1.75 m/s using the angular frequency and the wave number from the given wave function. Based on the presented calculations, none of the provided answer options (a, b, c, d) are correct.

Step-by-step explanation:

The student is asking for the speed of a wave given by the wave function y(x,t)=(3.00mm)sin[(4.00m−¹)x−(7.00s−¹)t]. To find the speed of the wave using the wave equation, we need to identify the wave number (k) and the angular frequency (ω) from the wave function. In this wave function, the wave number k is 4.00 m−¹, and the angular frequency ω is 7.00 s−¹. The wave speed v can be calculated by taking the ratio of the angular frequency to the wave number.

v = ω / k = (7.00 s−¹) / (4.00 m−¹) = 1.75 m/s

However, the answer options provided do not include 1.75 m/s. Since none of the choices match the calculated wave speed, either there is a typo in the question or in the provided options. Based on the presented calculations, none of the provided answer options (a, b, c, d) are correct.