## Transverse Waves

A transverse mechanical wave is traveling along a string lying along the x-axis. The displacement of the string as a function of position and time, y(x,t), is describe by the following equation:

y(x,t) = 0.0490 * sin(5.60x-185t)

where x and y are in meters and the time is in seconds. What is the velocity of the wave? (Define positive velocity along the positive x-axis.)

y(x,t) = 0.0490 * sin(5.60x-185t)

where x and y are in meters and the time is in seconds. What is the velocity of the wave? (Define positive velocity along the positive x-axis.)

**33.0 m/s**## **Approach**

The general equation for a traveling wave is:

y(x,t)=Asin(2*pi*f*t +or- 2pi/λ*x)

y(x,t)=Asin(2*pi*f*t +or- 2pi/λ*x)

**Solution**

Comparing the given equation with the general equation implies that 2πf = 185 and 2π/λ = 5.60. Thus both the frequency, f = 185/(2*π) Hz and wavelength, λ = 2*π/$k2f m, can be calculated. The speed is v = fλ = 33.0 m/s.